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CONTENTSVOL.2

18. Electrostatics

19. Current Electricity 1104-1204 (606)

20. Heating and Chemical Effect of Current 1205-1247 (302)

21. Magnetic Effect

22. Magnetism.

Page Number ofNo. Questions

..957-1103 (863)

f Current 1248-1326 (467)

.1327-1373 (319)

23. Electromagnetic Induction 1374-1432 (393)

24. Alternating Cur-ent 1433-1471 (239)

25. Electron, Photoi, Photo-electric Effect and X-Rays 1472-1537 (509)

26. Atomic and Nu lear Physics 1538-1632 (732)

27. Electronics. .1633-1715 (519)

28. Communicatioi 1716-1744 (118)

29. Ray Optics. .1745-1867 (850)

30. Wave Optics

31. Universe.

.1868-1941 (482)

.1942-1956 (87)

* • » » » • • * » * * »

* * * * * *

Chapter

18Electrostatics

Electric Charge

(1) Charge is the property associated with matter due to whichit produces and experiences electrjcal and magnetic effects.

(2) It is known that evei|y atom is electrically neutral,containing as many electrons a^ the number of protons in thenucleus.

(3) Charged particles can be created by disturbing neutrality ofan atom. Loss of electrons gives toositive charge (as then np > ne)and gain of electrons gives negative charge (as then ne > np) to aparticle. In charging mass of the bcjdy changes as shown below

A charged body may attract a neutral body or an oppositelycharged body but it always repels similarly charged body. Hence,repulsion is a sure test of electrification.

(5) Unit and dimensional formula

S.I. unit of charge is Ampere x sec = coulomb (C). smaller S.I.units are rr?C, //C.

C.G.S. unit of charge is Stat coulomb or electrostatic unit(e.s.u.) Electromagnetic unit of charge is ab coulomb

!C = 3xl09 stat coulomb = — ab coulomb .

Dimensional formula [Q] = [AT]

(6) Charge is

Transferable : It can be transferred from one body toanother.Associated with mass : Charge cannot exist without massbut reverse is not true.

Conserved : It can neither be created nor be destroyed.Invariant : Independent of velocity of charged particle.

(7) Electric charge produces electric field (E), magnetic field

(B) and electromagnetic radiations.

1 <M

Neutral

M

Fig.

v = 0v = constant v * constant

M">ME and B E , B and Radiates energy

(4) Charges with the same ele:trical sign repel each other, andcharges with opposite electrical sigrj attract each other.

_+ ,_

Fig. 18.2

Fig. 18.3(8) Point charge : A finite size body may behave like a point

charge if it produces an inverse square electric field. For examplean isolated charged sphere behave like a point charge at very largedistance as well as at very small distance close to it's surface.

(9) Charge on a conductor : Charge given to a conductoralways resides on it's outer surface. This is why both a solid andhollow conducting sphere of same outer radius will hold maximum

958 Electrostaticsequal charge. If surface is uniform the charge distributes uniformlyon the surface and for irregular surface the distribution of charge,i.e., charge density is not uniforjn. It is maximum where the radiusof curvature is minimum and vice versa, i.e., o°c (l/R). This is

why charge leaks from sharp points.

(A) (B)

Fifl. 18.4(10) Charge distribution : It may be of two types

(i) Discrete distribution of charge : A system consisting ofultimate individual charges.

Fig. 18.5(ii) Continuous distribution of charge : An amount of charge

distributes uniformly or non-uniformly on a body. It is of followingthree types

(a) Linear charge distribution : Charge on a line e.g. chargedit wire, circu

3 ChargeLength

^» S.I.

ar charged rinc

= Linear charge

cunit is —

m

etc.

density

Al

+ /I

-

+

Fig. 18.6(b) Surface charge distribution : Charge distributed on a

surface e.g. plane sheet of charge, conducting sphere, conductingcylinder etc.

a = — = Surface charge densityArea + + +

CS.I. unit is

m*

*Dimension is [L 2TA]Fig. 18.7

(c) Volume charge density : Charge distributes through out thevolume of the body e.g. charge on a dielectric sphere etc.

pCharge ... _,_ + +

p = ^— = Volume charge densityVolume

S.I. unit is

Dimension is [L~3TA] Fig. 18.8

(11) Quantization of charge : If the charge of an electron

(= 1.6 x 10~19C ) is taken as elementary unit i.e quanta of charge,the charge on any body will be some integral multiple of e i.e.,

Q = ± ne with n = 1,2,3....

Charge on a body can never be ± — e , ±17.2e or ±10~5e etc.ij

(12) Comparison of charge and mass : We are familiar withrole of mass in gravitation, and we have just studied some features ofelectric charge. We can compare the two as shown below

Table 18.1 : Charge v/s mass

Charge

(1) Electric charge can bepositive, negative or zero.

(2) Charge carried by a bodydoes not depend upon velocityof the body.

Mass

(1) Mass of a bodypositive quantity.

is always a

(2) Mass of a body increases with

/ 2 / 2

where c is velocity of light invacuum, m is the mass of the body

moving with velocity v and mg is

rest mass of the body.

(3) Charge is quantized.

(4) Electric charge is alwaysconserved.

(5) Force between charges canbe attractive or repulsive,accordingly as charges areunlike or like charges.

(3) The quantization of mass is yetto be established.

(4) Mass is not conserved as it canbe changed into energy and vice-versa.

(5) The gravitational force betweentwo masses is always attractive.

Methods of Charging

A body can be charged by following methods.

(1) By friction : By rubbing two bodies together, both positiveand negative charges in equal amounts appear simultaneously dueto transfer of electrons from one body to the other.

(i) When a glass rod is rubbed with silk, the rod becomespositively charged while the silk becomes negatively charged. Thedecrease in the mass of glass rod is equal to the total mass ofelectrons lost by it.

(ii) Ebonite on rubbing with wool becomes negatively chargedmaking the wool positively charged.

(iii) Clouds also get charged by friction.

(iv) A comb moving through dry hair gets electrically charged.It starts attracting small bits of paper.

(v) During landing or take-off, the tyres of an aircraft getelectrified therefore special material is used to manufacture them.

Fig. 18.9

(2) By electrostatic induction : If a charged body isbrought near an uncharged body, one side of neutral body (closerto charged body) becomes oppositely charged while the other sidebecomes similarly charged.

+Q +Q

+Q

Fig. 18.10

Induced charge can be lesser or equal to inducing charge (but

never greater) and its maximum value is given by Q'= -Q 1 -K

where Q is the inducing charge and K is the dielectric constant ofthe material of the uncharged body. It is also known as specificinductive capacity (SIC) of the medium, or relative permittivity er

of the medium (relative means with respect to free space)

Table 18.2 : Different dielectric constants

Medium

Vacuum

air

Paraffin Wax

Rubber

Transformer oil

Glass

K

1

1.0003

2.1

3

4.5

5-10

Medium

Mica

Silicon

Germanium

Glycerin

Water

Metal

K

6

12

16

50

80

CO

(3) Charging by conduction : Take two conductors, onecharged and other uncharged. Bring the conductors in contact witheach other. The charge (whether ~ve or +ve} under its ownrepulsion will spread over b<j>th the conductors. Thus theconductors will be charged with the same sign. This is called ascharging by conduction (through contact).

Electroscope

It is a simple apparatus by which the presence of electric chargeon a body is detected (see figure). Whenmetal knob is touched with a chargedbody, some charge is transferred to thegold leaves, which then diverges due torepulsion. The separation gives a roughidea of the amount of charge on thebody. When a charged body is broughtnear a charged electroscope, the leaveswill further diverge, if the charge onbody is similar to that on electroscopeand will usually converge if opposite. Ifthe induction effect is strong enoughleaves after converging may again F>9- 18.11diverge.

Coulomb's Law

Electrostatics 959

If two stationary point charges Q: and Q2 are kept at a

distance r, then it is found that force of attraction or repulsionbetween them is

Torsionfiber

Chargedballs

Scale

Fig. 18.12

Q,Q2F« ' 2" i.e., F = —L-2- (k = Proportionality constant)

InC.G.S. (for air ) k = 1, F = -^

In S.I. (for air) k = 1 - = 9xl09^L

=> F = . V2 newton (I Newton = 10s Dyne)4xe0 r

£0 = Absolute permittivity of air or free space

= 8.85 xl(T12n-m m

. It's dimensional formula

(1) Vector form of Coulomb's law : Vector form of

Coulomb's law is F 12 = K.O Q -*— - - r,0 -K.—1-^-2-fi2, where f12 is,2

the unit vector from first charge to second charge along the linejoining the two charges.

(2) Effect of medium : When a dielectric medium iscompletely filled in between charges, rearrangement of the chargesinside the dielectricmedium takes place and QI jjjfthe force between thesame two charges k— — r —decreases by a factor of p- jg jgK (dielectric constant)

1 Q,Q2i £> F = Q'r' medium ir . tr ' nK <ureQK ^

(Here £0K = E0eT - E = permittivity of medium)

If a dielectric medium (dielectric constant K, thickness t) ispartially filled betweenthe charges then Qi »;,< Q-effective air separationbetween the charges

becomes (r-t+t^/K) F'9-

Hence force F =1 QiQ2

(r-t + t

(3) Principle of superposition : According to the principle

of superposition, total force acting on a given charge due tonumber of charges is the vector sum of the individual forces acting

on that charge due to all :he Qcharges.

Electric Field

Consider n number of charges

Ql , Q2 , Q3 ... applying force on

a charge Q.

Net force on Q will be

Fnet =Fl+F2+.... + Fn-l+F

(4) The magnitude of the resultant of two electric forces is given by

F9 sin 6and tan a =

Fj + F2 cos 9

Fig. 18.16For problem solving remember following standard results.

Fig. 18.17Table 18.3 : Fundamental forces of nature

Force

Force ofgravitationbetween anytwo masses

Electromagnetic force (forstationaryand movingcharges)

Nuclear force(betweennucleons)

Weak force(for processeslike /? decay)

Nature andformula

Attractive, F =Gm^mz/r2,obey's Newton'sthird law ofmotion, it's aconservative forc)e

Attractive as wellas repulsive,obey's Newton's,third law ofmotion, it's aconservative force

Attractive, exactexpression is notknown till date.

(Attractive as wellas repulsive)Formula notknown

Range

Long range(betweenplanets,betweenelectron andproton)

Long (upto fewketometers)

Short (of theorder of nuclearsize 10-15 m)

Short

(less than andupto lCHGm)

Relativestrength

1

1036

1039

(strongest)

1024

A positive charge or a negative charge is said to create its fieldaround itself. Thus the space around a charge in which anothercharged particle experiences a force is said to have electric field in it.

Fig. 18.18

(1) Electric field intensity (£) :The electric field intensity at any point isdefined as the force experienced by aunit positive charge placed at that point.

e_ f _ f c Q-

Qo r

where q0 ~* 0 so tnat presence of this charge may not affect

the source charge Q and its electric field is not changed, thereforeexpression for electric field intensity can be better written as

£ = Lim •10 ~>o q0

(2) Unit and Dimensional formulanewton volt

Its S.I. unit = =-joule

coulomb meter coulomb x meter

and C.G.S. unit - dyne/stat coulomb.

Dimension : [E] ^MLT^A'1]

(3) Direction of electric field : Electric field (intensity) £is a vector quantity. Electric field due to a positive charge is alwaysaway from the charge and that due to a negative charge is alwaystowards the charge.

(4) Relation between electric force and electric field :

In an electric field E a charge (Q) experiences a force F = QE . If

charge is positive then force is directed in the direction of fieldwhile if charge is negative force acts on it in the opposite directionof field _ _

E ~—* £

Fig. 18.19(5) Superposition of electric field (electric field at a point

due to various charges) : The resultant electric field at any point isequal to the vector sum of electric fields at that point due to various

charges i.e. E = E^+ E2+ E3 +...

(6) Electric field due to continuous distribution ofcharges : A system of closely spaced electric charges forms acontinuous charge distribution. To find the field of a continuouscharge distribution, we divide the charge into infinitesimal chargeelements. Each infinitesimal charge element is then considered, as

a point charge and electric field dE is determined due to thischarge at given point. The net field at the given point is the

summation of fields of all the elements, i.e., £ = |d£ .

Electric Potential

(1) Definition : Potential at a point in a field is defined as theamount of work done in bringing a unit positive test charge, frominfinity to that point along any arbitrary path (infinity is point ofzero potential). Electric potential is a scalar quantity, it is denoted

byV;U'

V = —do

(2) Unit and dimensional formula

;ou/eS. I. unit: = volt

coulomb

C.G.S. unit: stqt volt (e.s.u.); |l volt =

Dimension : [V] = [MLT^/f1]

300siat volt

(3) Types of electric potential : According to the nature ofcharge, potential is of two types

(i) Positive potential : Due to| positive charge,

(ii) Negative potential: Due to negative charge.

(4) Potential of a system of point charges : Consider P isa point at which net electric potential is to be determined due toseveral charges. So net potential it P

zQilr3 r4

In general V = —

Fig. 18.20(5) Electric potential due to a continuous charge

distribution : The potential due to a continuous chargedistribution is the sum of potentials of all the infinitesimal chargeelements in which the distribution

= f_

may be divided i.e.,

(6) Graphical representation of potential : As we moveon the line joining two charges then variation of potential withdistance is shown below

+ q -q

0

Fig. 18

+ q

0

(7) Potential difference : In an electric field potentialdifference between two points A and B is defined as equal to theamount of work done (by external agent) in moving a unit positive

Wcharge from point A to point B i.e., VB - VA = —

UWVH8/U

Electrostatics 961 L||«s

Electric Field and Potential Due to VariousCharge Distribution

(1) Point charge : Electric field and potential at point P dueto a point charge Q is

Q0 — P< r >

Fig. 18.22

:—£ or L =K-fr ri

Graph

Fig. 18.23

(2) Line charge: Electric field and potential due to a chargedstraight conducting wire of length / and charge density A

•.A

fc* , .

V = —— log,2>^o

-r-> Pa v

Fig. 18.24

k/iand Ev = — (cos /? - cos a)

(i) If point P lies at perpendicular bisector of wire i.e. a = p,

2kAEr = sin or andE, = 0

it(ii) If wire is infinitely long i.e. / —> °° so a = ft = — ;

2kAr

= 0:

(iii) If point P lies near one end of infinitely long wire i.e. a = 0,

-./.-I

Fig. 18.25

962 Electrostatics(3) Charged circular ring : Suppose we have a charged

circular ring of radius R and charge Q.On it's axis electric field and potentialis to be determined at a poiht 'P'distance 'x' away from the centre ofthe ring.

At point P

kQxE =

(x2+R2)3 / 2Fig. 18.26

At centre x = 0 so £„,, ,„„ = C

At a point on the axis such that x » R E = kQ

= ± - , Em a x=V2

Graph

* R

Fig. 18.27(4) Some more results of line charge : If a thin plastic rod

having charge density /I is bent id the following shapes then electricfield at P in different situations is shown in the following table

Table 18.4 : Electric field due to bending of charged rod

f- r- 2U .£ = sin 6r

E = -

.-

P r ,

E = =^-cos0r

9Q1J90'

r |PE

11 +

2Ur

+ + + +

(5) Charged cylinder

(i) Non-conducting (ii) Conducting chargeduniformly charged cylinder cylinder

I

+l+

I+ -f

+lf

+!+. i j

++ P^_--

__ r «,

+

++++

+

iTiLr

1*1

. i ^

++T-

~+

+

- r

(A) (B)Fig. 18.28

If point of observation (P) lies outside the cylinder then for

both types of cylindrical charge" distribution Eout = , and

I r —A, .

If point of observation lies at surface i.e. r - R so for both

cylinders and Vsurface \o5e R + co" 2^f?0

If point of observation lies inside the cylinder then for conducting

cylinders Ein = 0 and for non-conducting £in = j-

Graph

E

O

E '

1

OEin=0

(A) For non-conducting cylinder (B) For conducting cylinder

Fig. 18.29

(6) Charged conducting sphere (or shell of charge) : Ifcharge on a conducting sphere of radius R is Q (and a = surfacecharge density) as shown in figure then electric field and potentialin different situations are

+Q+ + +

+Q

yf +

P

(A) Outside+ +

(B) At the surfaceFig. 18.30

(C) Inside

(i) Outside the sphere : If point P lies outside the sphere

1 Q oR2 1 Q '1*?2~5" = 5" and ^out = „ __ -~ = '

(Q = crxA = CTX4

(ii) At the surface of sphere : At surface r = R

1 Q a 1 Q oRSo, E s =- .-fV = — and Vs =- . = -

R en

(iii) Inside the sphere: : Inside the conducting chargedsphere electric field is zero and potential remains constant at allpoints and equals to the potential at the surface.

£,„ = 0 and Un = constant = V,

Graph

O

£

O r =R

(A)Fig. 18.31

(7) Uniformly charged non-conducting sphere : Suppose

charge Q is uniformly distributed in the volume of a non-

conducting sphere of radius R as shown below

+Q ?P i+Q +Q

(A) Outside (B) Af the surface (C) InsideFig. 18.32

(i) Outside the sphere : If point P lies outside the sphere

-.— and

If the sphere has uniform volume charge density p =

then Eout =pR3

3£or2 °M ~ 3£or

ere :(ii) At the surface of sphere : At surface r = R

(iii)

and

s - t

Inside

1\Jt£r\e

14*£

"rJlCr

Q

sphere

Qr

Q13R2

2R

pR ., 1 Q pR2

0

: At

pr3£0

HI 1U V - — . —

4^f0 R 3e0

a distance r from the centre

p(3R2-r2)3 f.F

Otg

At centre r = 0 so, Vce

4;r'E'o

i p V >V >Vi.e., v centre v surface ou>

Graph

O r = R

(B)Fig. 18.33

(8) Infinite thin plane sheet of charge : Consider a thin

infinite non-conducting plane sheet having uniform surface charge,,, , . ,. .

density a . Electric field and potential near the sheet are

and V = -— + C

(9) Electric field due to two thin infinite plane parallelsheets cf charge : Consider two large uniformly charged parallelplates A and B, having surface charge densities ffA and <JB

n _respectivelu Net electric field at points P, Q and R is to becalculated.'

B ^fjr *

* *

*+ >

Fig. 18.35

At P, Ep = -(£A + EB ) = - - — (<JA + a

AtQ, E0=|

l

-0-R

At /?, ER = (EA + EB) = (ffA + CTB)2e0

Special cases

(i) If aA = aB = (Tthen \EP\R\ O/£Q and EQ = 0

(ii) If aA = crand aB = - crthen £P = ER = 0 and £0 =

(10) Hemispherical charged body

At centre O, £ = -2—

V = -2£ Fig. 18.36

Uniformly charged disc : At a distance x from centre

O on it's axisa

iT V

£ =

If x -* 0, E-=2en

Fig. 18.37

i.e. for points situated near the disc, it

behaves as an infinite sheet of charge.

964 Electrostatics(12) Charged conducting surface : Electric field A and

potential near a charged conducting surface.

Potential Due to Concentric Spheres

r2r2

(1) Consider two concentrip conducting shells of radii rj andrj carrying uniformly distributed charges Ql and Q2

respectively. Potential at the surface of each shell is

1 1

V2 =

b| r2

Q2

Fig. 18.38(2) The figure shows three conducting concentric shells of radii

a, b and c (a < b < c) having charges Q0, Qb and Qc respectively

Potential at A;

1 9s.a

Potential at B;

1

Potential at C;~Q0

Vc = H •C C

Fig. 18.39

(3) The figure shows two concentric spheres having radiiand r2 respectively (r2 > rt). Ifouter sphere is earthed then

(i) Potential at thesurface of outer sphere

9.r->

pharge on inner sphere is +Q and

V2 = .^---.Q

=> Q' = -Qii) Potential of the inner sphere

1 (-0) Q,fl + -V1 =

(4) In the above case if outer sphere is given a charge +Q andinner sphere is earthed then

(i) In this case potential at the surface of inner sphere is zero, so

+Qif Q' is the charge induced on inner sphere

1then

i.e.,

(Charge on inner sphere isFig. 18.41

less than that of the outer sphere.)

(ii) Potential at the surface of outer sphere

1 Q' , 1 £r,

V2 =0 o

Relation between Electric Field and Potential

(1) In an electric field rate of change of potential with distanceis known as potential gradient.

(2) Potential gradient is a vector quantity and it's direction isopposite to that of electric field.

(3) Potential gradient relates with electric field according to thedV

following relation £ = — — . This relation gives another unit ofdr

electric field asvolt

meter

(4) In the above relation negative sign indicates that in thedirection of electric field, potential decreases.

(5) Negative of the slope of the V-r graph denotes intensity ofV

electric field i.e. tan 6 = — = -Er

(6) In space around a charge distribution we can also writep _ : _ - _ . " „ 9V ^ dV . ., 3Vfc = Exi +tvj + tzfc , where hx = , hy = andhz =

dV(7) With the help of formula E = , potential difference

drbetween any two points in an electric field can be determined by

knowing the boundary conditions dV = — I E.dr = -l E.drcosffJri Jri

(8) If at any point £ = 0 , then V may or may not be zero. Forexample, inside a charged conductor E = 0 . but V is not zero.

(9) If at any point E = 0 , then V = constant (zero or nonc dV

zero) because E = .dr

(10) If V = 0 at a point, then E may or may not be zero. Forexample, on the equatorial line of a dipole V = 0 , but £ * 0 .

Electric Lines of Force(1) Definition : The electric field in a region is represented by

continuous lines (also called lines of force). Field line is animaginary line along which a positive test charge will move if leftfree.

(A) (Radially outward)

Fig. 18.42

(2) Properties of electric lines of force

(i) Electric field lines come out of positive charge and go intothe negative charge.

(ii) Tangent to the field line at any point gives the direction ofthe field at that point.

(iii) Field lines never intersect

(iv) Field lines are always

Fig. 18.43

ct each other,

normal to conducting surface.

(B)Fig. 18.44

(v) Field lines do not exist ifliside a conductor.

(vi) The electric field linesj never form closed loops. (Whilemagnetic lines of forces form closed loop)

(vii) The number of linescharge is proportional to the magnitude of charge i.e. |Q|number of lines. In the following figure | QA \>\B \ B

originating or terminating on a

(viii) If the lines of forces a|re equidistant and parallel straightlines, the field is uniform andi if either, lines of force are notequidistant or straight line or balso the density of field lines is proportional to the strength of theelectric field.

,Y

(A) £x = £y

Fig

ith, the field will be non uniform,

(B) Ex

18.46

Equipotential Surface

For a given charge distribution, locus of all points having samepotential is called "equipotential surface" regarding equipotentialsurface following points should keep in mind :

(1) The density of the equipotential lines gives an idea aboutthe magnitude of electric field. Higher the density larger the fieldstrength.

(2) The direction of electric field is perpendicular to theequipotential surfaces or lines.

(3) The equipotential surfaces produced by a point charge ora spherical charge distribution are a family of concentric spheres.

V = V,V4 }/5

V= V,

Spherical E.P.S.for a point charge

Equipotential, surface

Fig. 18.47

(4) For a uniform electric field, the equipotential surfaces are afamily of plane perpendicular to the field lines.

(5) A metallic surface of any shape is an equipotential surface.

(6) Equipotential surfaces can never cross each other

(7) The work done in moving a charge along an equipotentialsurface is always zero.

Motion of Charged Particle in Electric Field

(1) When charged particle initially at rest is placed inthe uniform field

Suppose a charged particle having charge Q and mass m isinitially at rest in an electric field of strength E. The particle willexperience an electric force which causes it's motion.

(i) Force and acceleration : The force experienced by thecharged particle is F = QE .

Acceleration produced by this force is a = — = —QEm

(ii) Velocity : Suppose at point A particle is at rest and intime t it reaches the point B where it's velocity becomes u. Also ifAV = Potential difference between A and B, S = Separationbetween A and B

-'EQEt |2QAVm

Fig. 18.48

( i i i ) Momentum : Momentum p = mu, p = mx = QEtm

966 Electrostatics

(iv) Kinetic energy : Kinetic energy gained by the particle in

time t is K = — mv2 = —2 2

QB

m

„ 1 2QAV „.,.or K = — mx—^ = Q&Vm

(v) Work done : Accordingsay that gain in kinetic energy =

2m

:o work energy theorem we canwork done in displacement of

charge i.e. W = QAV

where AV = Potential difference between the two positions of

charge Q. ( AV = E .A r = EArcostf where 9 is the angle between

direction of electric field and direct on of motion of charge).

If charge Q is given a displacement r =(^1 +r2j + r3k) in an

electric field £ = (Eji +E2; +£3fc), the work done is

IV = Q(E .7) = + E2r2 + E3r3

Work done in displacing a charge in an electric field is pathindependent because electric force field is conservative.

W, = W,, = IV,,,

Fig. 18.49

(2) When a charged particle enters with an initialvelocity at right angle to the uniform field

When charged particle enters perpendicularly in an electricfield, it describes a parabolic path <

(i) Equation of trajectory :has uniform velocity along x-axis and horizontal displacement (x) isgiven by the equation x = ut

Since the motion of the particle is accelerated along y-axis

s shown

Throughout the motion particle

X

Fig. 18.50

So y = — I — ; this is the equation of a parabola21 rr> \ I

which shows y <

(ii) Velocity at any instant : At any instant t, vx = u and

QEt

If ft is the angle made by v with x-axis then

mu

Equilibrium of Charges(1) Definition : A charge is said to be in equilibrium, if net

force acting on it is zero. A system of charges is said to be inequilibrium if each charge is separately in equilibrium.

(2) Types of equilibrium : Equilibrium can be divided infollowing types:

(i) Stable equilibrium : After displacing a charged particlefrom it's equilibrium position, if it returns back then it is said to bein stable equilibrium. If U is the potential energy then in case of

stable equilibriumd2U

dx2is positive i.e., U is minimum.

(ii) Unstable equilibrium : After displacing a chargedparticle from it's equilibrium position, if it never returns back then itis said to be in unstable equilibrium and in unstable equilibrium

d2U

dx2is negative i.e., U is maximum.

(iii) Neutral equilibrium : After displacing a charged particlefrom it's equilibrium position if it neither comes back, nor movesaway but remains in the position in which it was kept then it is said

to be in neutral equilibrium and in neutral equilibriumdx2

zero i.e., U is constant

Table 18.5 : Different cases of equilibrium of charge

Suspended charge

Freely suspended charge

£ t F = QE In equilibrium

+Q

Q

Suspension of charge fromstring

In equilibrium

Tsin6> = QE ....(i)

Tcos# = mg ....(ii)

From equations (i) and (ii)

T = V(QE)2+(mg)2

QEand tan 6 =mg

System of three collinearcharges

In the following figure three

charges Q1? Q and Q2 are kept

along a straight line, charge Q

will be in equilibrium if and

only if

| Force applied by charge Qi |= | Force applied by charge Q2 |

i.e. Q2Q

This is the necessary conditionfor Q to be in equilibrium.

If all the three charges (Qj, Q

and Q2) are similar, Q will be

in stable equilibrium.

If extreme charges are similar

while charge Q is of different

nature Q will be in unstable

equilibrium.

Time Period of Oscillation of a Charged Body

(1) Simple pendulum : If a simple pendulum having length /and mass of bob m oscillates atiout it's mean position then it's time

period of oscillation T = 2n\—

•aFig. 18.52

Case-1 : If some charge say +Q is given to bob and anelectric field E is applied in the | direction as shown in figure, thenequilibrium position ot charged bob (point charge) changes from OtoCX. _ "

Fig. 18.53

On displacing the bob from it's equilibrium position 0' it willoscillate under the effective acceleration g7, where

g' = V(mg)2+(QE)2 => d' = 32 + (QE I rnf . Hence the

So new time period

Ig + (QE/m)

T2 <T

new time period is T, = "in \ = 2jc\9'

Since g' >g, so Tj < T i.e. time period of pendulum will decrease.

Case-2 : If electric field is applied in the downward directionthen effective acceleration

Fig. 18.54

Case-3 : In case 2 if electric field is applied in upwarddirection then, effective acceleration ^^^^

g' = g-QE/m Kx QE

So new time period

T3 =

T 3 > T

IS-(Q£/m)

(2) Charged circular ring

Fig. 18.55

: A thin stationary ring of radius Rhas a positive charge +Q unit. lit a negative charge - q (mass m) isplaced at a small distance x fron the centre. Then motion of theparticle will be simple harmonic motion.

, _. „Having time period T = 2n

Qi

Fig. 18.56

(3) Spring mass system : A block of mass m containing anegative charge - Q is placed on a frictionless horizontal table andis connected to a wall through an unstretched spring of springconstant k as shown. If electric field E is applied as shown in figurethe block experiences an electric force, hence spring compress andblock comes in new position. This is called the equilibrium positionof block under the influence of electric field. If block is compressedfurther or stretched, it executesoscillation having time period

£

m,-QT = 2x.\ . Maximum

V k

compression in the spring due to

QE Fig. 18.57electric field = —

Neutral Point and Zero PotentialA neutral point is a point where resultant electrical field is zero.

(1) Neutral point Due to a system of two like pointcharges : For this case neutral point is obtained at an internalpoint along the line joining two like charges.

NQ, Q2

• X 2 -

Fig. 18.58If N is the neutral point at a distance Xj from

distance x 2 (=x -Xj ) from Q2 then

AtN |E.F. due to QJ = |E.F. due to Q2|

and at a

i.e.,

Short Trick : x-, = -

\

X

Q2- ±1

and x2=-r

(2) Neutral point due to a system of two unlike pointcharge : For this condition neutral point lies at an external pointalong the line joining two unlike charges. Suppose two unlikecharge Ql and Q2 are separated by a distance x from each other.

QiN. Q,

Fig. 18.59

Here neutral point lies outside the line joining two unlike chargesand also it lies nearer to charge which is smaller in magnitude.

968 Electrostatics

If Qi| < Q2j then neutral point will be obtained on the side of

, suppose it is at a distance / from Qj

Hence at neutiol point —^- i

so 1 =

kQ2 9L.(-L{Q2

(3) Zero potential due to a system of two point charges

(i) If both charges are like then resultant potential is not zero atany finite point.

(ii) If the charges are unequal and unlike then all such pointswhere resultant potential is zero lie on a closed curve.

(iii) Along the line joining the two charge, two such pointsexist, one lies inside and the other lies outside the charges on theline joining the charges. Both the above points lie nearer to thesmaller charge.

For internal point

(it ib cibbumeu mm | Vi I "' | V2

At P * 2' I \I v- V I

i \~xi)

X

(QJJ/QJ + 1)

For External point

A+ D Qj Q2

xi (x + xj

X

Electrostatic Potential En

i.

Qi p Q2

HI • Ok

Fig. 18.60

p Qi Q2

•e-x -**

Fig. 18.61

ergy_____(1) Work done in bringing the given charge from infinity to a

point in the electric field is known as potential energy of thecharge. Potential can also be written as potential energy per unit

, . W Ucharge, i.e. V = — = — .

(2) Potential energy of a system of two charge

Potential energy of Qi = Potential energy of Q2 = potential

energy of system U = k- Q2

B

InC.G.S.Fig. 18.62

(3) Potential energy of a system of n charge

t, n OOti • • I T T * ~-^ V/Vr ,It is given by U = — V ; fc=

The factor of — is applied only with the summation sign

because on expanding the summation each pair is counted twice.

For a system' of 3 charges U = kV r!2 '23

(4) Work energy relation : If a charge moves from oneposition to another position in an electric field so it's potentialenergy change and work done by external force for this change isW = Uf - U,

(5) Electron volt (eV) : It is the smallest practical unit ofenergy used in atomic and nuclear physics. An electron volt isdefined as "the energy acquired by a particle having one quantumof charge (le), when accelerated by luo/t" i.e.

leV = 1.6xl(T19Cx— =1.6xl(rI9J = 1.6 x lO"12 erg\^f

(6) Electric potential energy of a uniformly chargedsphere : Consider a uniformly charged sphere of radius R havinga total charge Q. The electric potential energy of this sphere isequal to the work done in bringing the charges from infinity to

3Q2assemble the sphere. U =

0 R

(7) Electric potential energy of a uniformly charged thin

Q2spherical shell : It is given by the following formula U =

(8) Energy density : The energy stored per unit volumearound a point in an electric field is given by

LL =- = — £nE2 . If in place of vacuum some mediumVolume 2

is present then Ue =—£0£rE2

Force on a Charged Conductor

To find force on a charged conductor (due to repulsion of likecharges) imagine a small part XY to be cut and just separated fromthe rest of the conductor MLN. The field in the cavity due to therest of the conductor is E2, while field due to small part is Er. Then

Fig. 18.63

Inside the conductor £ = El - E2 = 0 or El = E2

Outside the conductor E = E1 + E2 = —

Thus Ej = £2 =

(1) To find force, imagine charged part XV (having chargeddA placed in the cavity MN having field E2). Thus force

2dF = (crdA)E2 or dF = dA . The force per unit area or

electrostatic pressure p = — =dA 2en

Electrostatics 969

(2) The force is always outwards as (±<r)2 is positive i.e., Electric Dipole

whether charged positively

expand the charged body.

or negatively, this force will try to

[A soap bubble or rubber balloon

expands on charging to it (charge of any kind + or -)].

Equilibrium of Charged Soap Bubble

(1) For a charged soap babble of radius R and surface tension T

and charge density a. The pressure due to surface tension 4 —R

and atmospheric pressure Fout acts radially inwards and the

electrical pressure (Pel) acts radially outwards.

(A) Uncharged bubble (B) Charged bubble

Fig 18.64

(2) The total pressure insidp the soap bubble

47 a2P - P t" in ~ rout T r>n

(3) Excess pressure inside t ne charged soap bubble

P. -P = P =-in out excess 2e0

(4) If air pressure inside and outside are assumed equal then

Pin=Pouti.e., Pexcess = 0 . So,

(i) Charge density : Since <7=.2T

R V^W?

(ii) Radius of bubble R =

(iii) Surface tension T =

(iv) Total charge on the bubble Q = 8xRj2e0TR

(v) Electric field intensity at tlfie surface of the bubble

r8T

[£0R V R

(vi) Electric potential at the siirface V = •

System of two equal and opposite charges separated by asmall fixed distance is called a dipole.

Axial line

Fig. 18.65

(1) Dipole moment : It is a vector quantity and is directed

from negative charge to positive charge along the axis. It is

denoted as p and is defined as the product of the magnitude of

either of the charge and the dipole length i.e. p = q(2l)

Its S.I. unit is coulomb-metre or Debye (1 Defaye = 3.3 x10~30 C x m) and its dimensions are

(2) When a dielectric is placed in an electric field, its atoms ormolecules are considered as tiny dipoles.

(A) (B)Fig. 18.66

Water (H2O), Chloroform (CHC/3), Ammonia (NH3), HCl, COmolecules are some examples of permanent electric dipole.

Fig. 18.67

(3) Electric field and potential due to an electric dipole :If a, e and g are three points on axial, equatorial and generalposition at a distance r from the centre of dipole

£

-<J

\• 9+ a

_ -1 -\ m

-21-

Fig. 18.68(i) At axial point: Electric field and potential are given as

_ 2/cpr kp

if r »/ then, EQ = —-. -|- (directed from - q to +q)

V=- -.-*=-. Angle between E0 and p is 0°.

(ii) At equatorial point: Eequatoria, =kp

|2*3/2

if r»l then, Ee = ,-^- directed from +q to - q) and

Ve = 0 . Angle between Ee and p is 180°.

(iii) At general point : E, and

*—2—• Angle between E and p is (6 + a) (where

tan or = — tan 9 )2

(4) Dipole in an external electric field : When a dipole is

kept in a uniform electric field. The net force experienced by the

dipole is zero as shown in fig.

The net torque experienced by the dipole is

T = pE sin 9

r = px£

Fig. 18.69Hence due to torque so produced, dipole aligns itself in the

direction of electric field. This is the position of stable equilibriumof dipole.

(i) Work done in rotation : Suppose initially, dipole is keptin a uniform electric field at an angle 6^. Now to turn it through anangle ff2 (with the field) Work done IV = pEfcos 0l - cos 92].

Fig. 18.70If d-i = 0° and 6^ = 6 i.e. initially dipole is kept along the field

then it turn through 9 so work done W = pE(l - cos 9)

(ii) Potential energy of dipole : It is defined as work donein rotating a dipole from a direction perpendicular to the field tothe given direction, i.e. from above formula of work.

If 9l = 90° and <% = 9 => W =* U = -pE cos 0 = -p . E

—*Stable equilibriumr = 0

P0=90U 0=180°Not in equilibrium Unstable equilibrium

rmax = f

W = pET=0

= 2pE= pE

(iii) Equilibrium of dipole : When 9 = 0° i.e. dipole is

placed along the electric field it is said to be in stable equilibrium,

because after turning it through a small angle, dipole tries to align

itself again in the direction of electric field.

When 6 = 180° i.e. dipole is placed opposite to electric field, it

is said to be in unstable equilibrium.

(iv) Oscillation of dipole : In a uniform electric field if a

dipole is slightly displaced from it's stable equilibrium position it

executes angular SHM havino period of oscillation.

n~T = 2x I — where / = moment of inertia of dipole about

VPE

the axis passing through it's centre and perpendicular to it's length.

(5) Electric dipole in non-uniform electric field : Innon-uniform electric field F

In this case motion of the dipole is combination of translatory

and rotatory motion

Table 18.6 : Dipole-dipole interaction

Relative position of dipole

-q +q -q +qw — - — * , — KJ

Pi Pi

+q d +<3d

— * — >

Pi Pz

-<* : -<*4

f-N,-q +q

-> ^-&Pi _, ***

Pz

Force

1 6ptp2

te0 r4

(attractive)

1 3pip2

4^r0 ' r4

(repulsive)

1 3p:p2

4;z£n ' r4

(perpendiculart o r )

Potentialenergy

1 2p,p2

4^o ^

1 PiP2

4^0' r3

Electric flux is a measure of 'flow' of electric field through asurface. It is equal to the product of an area element and the

~Lperpendicular component of l:., integrated over a surface.

(1) Flux of electric field E through

any area A is defined as.

i/> = E.AcosO or

(2) In case of variable elecjtric field or

curved area. <z> = \E.dA

(3) It's S.I. Unit is (Volt X m) orN-m2

(4) For a closed body oilitward flux is taken to be positivewhile inward flux is taken to be negative.

Negative flux

Gauss's Law and it's Application

(1) According to this law,

surface called Gaussian surface

physical surface, it can also bethe charge enclosed by

(2) Electric field in cjE. dA

8.73

IB total flux linked with a closed

(The surface need not be a real

n hypothetical one) is (1/£0) timesthe closed surface i.e.,

is complete electric field. It may be

partly due to charge with in thej surface and partly due to chargeoutside the surface. However if i

Gaussian surface, then

(3) The electric field E is re

inside and those outside the Gau

(Keep in mind, the electricGaussian surface contributes zeBecause as many lines due to thait).

lere is no charge enclosed in the

) .

ulting from all charge, both those

sian surface.

ield due to a charge outside theo net flux through the surface,charge enter the surface as leave

+0 -QT>

£Fig. 18.74

Flux from surface S1 = + —, Flux from surface S2 = - — ,

and flux from S3= flux from surface S4 = 0

Application of Gauss's law : See flux emergence in thefollowing cases

(1) If a dipole is enclosed by a surface

vQe n c=0

=> 0 = 0 R9- 18'75

(2) The net charge Qenc is the algebraic sum of all the enclosedpositive, and negative charges. If Qenc is positive the net flux isoutward; if Q ,. is negative, the net flux is inward.

-Q

(3) If a closed body (not enclosing any charge) is placed in anelectric field (either uniform or non-uniform) total flux linked with itwill be zero

(A) <pT = 0 (B) fa = <pout = EC? => fa = 0

Fig. 18.77

(4) If a hemispherical body is placed in uniform electric fieldthen flux linked with the curved surface is calculated as follows

^Curved + ^Circular = °

^Curved ~ ~0Circular

= -(Ex;rf?2cosl80°)

Fig. 18.78

972 Electrostatics(5) If a hemispherical body is placed in non-uniform electric

field as shown below, then flux ijinked with the circular surfacecalculated as follows

^Circular = "^Curved

= -2nR2EFig. 18.79

(6) If charge is kept at the centre of cube

1= — -(Q)

Fig. 18.80(7) If charge is kept at the centre of a face : First we should

enclosed the charge by assuming a Gaussian surface (an identicalimaginary cube)

Fig. 18.81

Total flux emerges from the sy

Q

(B)

item (Two cubes) 0tota/ = Q

Rux from given cube (i.e. frorri 5 face only) (f>cube =

(8) If a charge is kept at the cohier of a cube

total flux from the 8 cube system i

'••

pi...

(B)

Fig. 18.82

For enclosing the charge seven more cubes are required so

= —. Flux from given cube

<t>cube = •——. Flux from one face opposite to charge, of the given8e,

cube

Q/8f0 _ Q luse only three faces are seen).

(9) A long straight wire of charge

density /I penetrates a hollow body.

The flux emerges from the body is

A x Length of the wire inside bddy Fig. 18.83

Capacitance

(1) Capacitance of a conductor : Charge given to a

conductor increases it's potential i.e., Q <* V => Q = CV

Where C is a proportionality constant, called capacity orcapacitance of conductor. Hence capacitance is the ability ofconductor to hold the charge.

Coulomb _ , ._.(2) Its S.I. unit is — = Farad (F)

Volt

Smaller S.I. units are mF, /jF, nF and pF (lmF=10~3F,

Iff = lO^F , InF = 10~9F , IpF = 1/yf = 10"12F )

(3) It's C.G.S. unit is StatFarad IF = 9xlOn Stat Farad .

(4) It's dimension : [C] = [M^r2T4A2] .

(5) Capacity of a body is independent of charge given to thebody or it's potential raised and depends on shape and size only.

(6) Capacity of an isolated spherical conductor : Whencharge Q is given to a spherical conductorof radius R, then potential at the surface of

,Q

sphere is V =R V

1

++

o

9xlOy•R Fig. 18.84

If earth is assumed to be a conducting sphere having radius

R - 6400 km. It's theoretical capacitance C = 711/zF . But for all

practical purpose capacitance of earth is taken infinity and its

potential V = 0.

Combination of Charged Drops

Suppose we have n identical drops each having Radius - r,Capacitance - c, Charge - q, Potential - u and Energy - u.

If these drops are combined to form a big drop of Radius - R,

Capacitance - C, Charge - Q, Potential - V and Energy - U then

(1) Charge on big drop : Q = nq

(2) Radius of big drop : Volume of big drop = n x volume

of a single drop i.e., — ;rf?3 = nx — nr3 , R = n1/3ro o

(3) Capacitance of big drop : C = n1/3c

Q(4) Potential of big drop : V = — = -C n

(5) Energy of big drop : U = -CV2 = i(n1/3c)(n2/3u)2Lt £

(6) Energy difference :than the total energy all smaller drop. Hence energy difference

U = n5/3u

'otal energy of big drop is greater

rf1

(7) Surface charge densi

«•- Q

I ~ -1 0~, •>

I n 2 / 3 J

4;rr

n q q 1 0 "

4;rR2 »1Mrr 4nrz

Redistribution of Charges and Loss of EnergyWhen two charged condu<:tors are joined together through a

conducting wire, charge begins to flow from one conductor toanother from higher potential td lower potential.

This flow of charge stops when they attain the same potential.

Due to flow of charge, loss of energy also takes place in theform of heat through the connecting wire.

Suppose there are two spherical conductors of radii TJ and

r2, having charge Ql and Q2, potential Vj and V2, energies Uj

and U2 and capacitance C\d C2 respectively.

Q2

C2

V2

U2

Q2= C2V2

Fig. 18.85If these two spheres are ccnnected through a conducting wire,

then alteration of charge, potential and energy takes place.

Qi'C;

V

U,' •

Qi'=C,V

(1) New charge : Accord

* Q/r2 C2

1 VU,'

Q2'=C2V

Fib. 18.86

ng to the conservation of charge

Q! + Q2 = Qi + Q2 4 Q (say), also —L = —3- = iQ2 C2 r2

=* Q 2 =Q and similarly Ql = Q

(2) Common potential : Common potential

Total charge Ql + Q2 _ Qt + Q2 -iVi+C2V2

Total capacity ! Cj + C2 ~ Cl + C2 Cl + C2

(3) Energy loss : The k ss of energy due to redistribution ofcharge is given by

ripA f T - r r r r . M*-2(C, + C2)

(Vi-v2)2

Capacitor or Condenser(1) A capacitor is a device that stores electric energy or a

capacitor is a pair of two conductors of any shape, which are closeto each other and have equal andopposite charge.

(2) The capacitance of acapacitor is defined as themagnitude of the charge Q on thepositive plate divided by themagnitude of the potential difference

1.

Vbetween the plates i.e., C = •

J ^Fig. 18.87

(3) A capacitor get's charged when a battery is connectedacross the plates. Once capacitor get's fully charged, flow of chargecarriers stops in the circuit and in this condition potential differenceacross the plates of capacitor is same as the potential differenceacross the terminals of battery.

(4) Net charge on a capacitor is always zero, but when wespeak of the charge Q on a capacitor, we are referring to themagnitude of the charge on each plate.

(5) Energy stored : When a capacitor is charged by avoltage source (say battery) it stores the electric energy. If C =Capacitance of capacitor; Q = Charge on capacitor and V =Potential difference across capacitor then energy stored in

2 =\W ~capacitor U-

In charging capacitor by battery half the energy supplied isstored in the capacitor and remaining half energy (1/2 QV) is lost inthe form of heat.

Dielectric

Conductor(Metal foil)

Conductor(Metal foi

Dielectric(Plastic sheet)

Dielectrics are insulating (non-conducting) materials whichtransmits electric effect without conducting.

Dielectrics are of two types

(1) Polar dielectrics : A polar molecule has permanent

electric dipole moment (p) in the absence of electric field also. But

a polar dielectric has net dipole moment zero in the absence ofelectric field because polar molecules are randomly oriented asshown in figure.

Fig. 18.88

In the presence of electric field polar molecules tends to lineup in the direction of electric field, and the substance has finitedipole moment e.g. water, Alcohol, 00%, NH3, HC1 etc. are

made of polar atoms/molecules.

974 Electrostatics

(2) Non polar dielectric : In non-polar molecules, Eachmolecule has zero dipole momertt in its normal state.

When electric field is applied, molecules becomes inducedelectric dipole e.g. N2, O2, Benzene, Methane etc. are made ofnon-polar atoms/molecules

In general, any non-conducting material can be called as adielectric but broadly non-conducting material having non-polarmolecules referred to as dielectric.

(3) Polarization of a dielectric slab : It is the process ofinducing equal and opposite charges on the two faces of thedielectric on the application of electric field.

Fig. 18.89

(i) Electric field between the plates in the presence of dielectricmedium is E' = E - Ef where E =± Main field, E' = Induced field.

(ii) Dielectric constant of dielectric medium is defined as :

E _ Electric field between the plates with air „E' Electric field between the plates with medium

(iii) K is also known as relative permittivity (£r) of the

material or SIC (Specific Inductive Capacitance)

(4) Dielectric breakdown and dielectric strength : If avery high electric field is created ih a dielectric,. The dielectric thenbehaves like a conductor. Th;is phenomenon is known asdielectric breakdown.

The maximum value of electric field (or potential gradient)te without it's electric breakdownthat a dielectric material can tolera

is called it's dielectric strength.

S.I. unit of dielectric strength

unit iskV

Vof a material is — but practical

Capacity of Various Capacitor

(1) Parallel plate capacitor : It consists of two parallelmetallic plates (may be circular, rectangular, square) separated bya small distance. If A = Effective overlapping area of each plate.

(i) Electric field between the plates : E = — = -£Q A£Q

(ii) Potential difference between the plates : V = Exd = -

(iii) Capacitance : C = C.G.S. : C =

(iv) If a dielectric medium of dielectric constant K is hcompletely between the plates then capacitance increases by

times i.e. C'=KC

(v) The capacitance of parallel plate capacitor depends on A

(C <* A) and d C °= — . It does not depend on the charge on the

plates or the potential difference between the plates.

(vi) If a dielectric slab is partially filled between the plates

C' =£0A

(vii) If a number of dielectric slabs are inserted between theplate as shown jr jf _Jf jgr *

.~—S

'2 (3

d

C' =

Fig. 18.91

£0A

d-(t1+t2+t3+K

(viii) When a metallic slab is inserted between the plates

c=-e°A(d-t)If metallic slab fills the

complete space between the plates(i.e. t = d) or both plates arejoined through a metallic wire thencapacitance becomes infinite. |« ^ >|

Fig. 18.92

(ix) Force between the plates of a parallel plate capacitor.

Qz CV2

2£o 2£0A 2d

(x) Energy density between the plates of a parallel plate capacitor

Energy _ 1 2_.Energy density =

Volume

fable 18.7 : Variation of different variable (Q.CV.E and U)of parallel plate capacitor when dielectric is introduced

Quantity

Capacity

Charge

Potential

Intensity

Energy

C' = ,

£' = E/K

U' = UIK

Battery Remainsconnected

C' = KC

= v£' = £

U" = KU

(2) Spherical capacitpr : It consists of two concentricconducting spheres of radii a and b (a < b). Inner sphere is givencharge +Q; while outer spheri is earthed

(i) Potential difference : Between the spheres is

Q

(ii) Capacitance : C = 4/Z£

"/ . ! - ,

ab

' b-a

In C.G.S. C =ab

+Q

Fig. 18.93. In

b-a

(dielectric constant K) between

the presence of dielectric medium

he spheres C' =

(iii) If outer sphere is giverearthed

Induced charge on the inn

abb-a

a charge +Q while inner sphere is

:r sphere

Q' = — .Q and capacitancte ofb

the system C' =b-a

This arrangement is not a

Fig. 18.94

capacitor. But it's capacitance isequivalent to the sum of capacitance of spherical capacitor and

spherical conductor i.e. 4fi£0.—f— = 4^e0 + n£0bbY~a b-a

(3) Cylindrical capacitor : It consists of two co-axialcylinders of radii a and b (a <\b), inner cylinder is given charge+Q while outer cylinder is e|arthed. Common length of thecylinders is / then

Fig. 18.95

Electrostatics 975

Grouping of Capacitors(1) Series grouping(i) Charge on each capacitor remains same and equals to the

main charge supplied by the battery but potential differencedistributes i.e. V = Vl + V2 + V3

(ii) Equivalent capacitance

- = - + - + or c = (C +c +C1)"1

Cj C2 C3

f -Q +Q -Q +Q -Q

+ 1 , -

Fig. 18.96(iii) In series combination potential difference and energy

distributes in the reverse ratio of capacitance i.e.,

V « — and U °= — .C C

(iv) If two capacitors having capacitances Cl and C2 areC,C, Multiplication

connected in series then C,~ = — =C, + C2 Addition

and v2 =

(v) If n identical capacitors each having capacitances C areconnected in series with supply voltage V then Equivalent

Ccapacitance C = — and Potential difference across each

nV

capacitor V' = — .n

(vi) If n identical plates are arranged as shown below, theyconstitute (n - I) capacitors in series. If each capacitor has

capacitance —— then Ceq = —!

Fig. 18.97

In this situation except two extreme plates each plate iscommon to adjacent capacitors.

(vii) Here, effective capacitance Ceq is even less than the least

of the individual capacitances.(2) Parallel grouping(i) Potential difference across each capacitor remains same

and equal to the applied potential difference but charge distributesi.e. Q = Q! + Qz + Q3 +Qi -

(ii) Ceq = C, + C2 + C3

(iii) In parallel combination charge and energy distributes inthe ratio of capacitance i.e. Q <x C and U <* C

(iv) If two capacitors having capacitance G\d C2 respectivelyare connected in parallel then Ce + C

Qi = . Q and Q2 = .Q

(v) If n identical capacitors are connected in parallel, thenEquivalent capacitance Ce = nC and Charge on each

capacitor Q = Q—

If n identical plates are arranged such that even numbered ofplates are connected together and odd numbered plates areconnected together, then (n - 1) capacitors will be formed and theywill be in parallel grouping. r _

Fig. 18.99Equivalent capacitance C' = (in -1) C

£ Awhere C = capacitance of a capacitor = -2—

d

(vi) This type of combination is used when high capacity isrequired at low potential.

(vii) If Cp is the effective capacity when n identical capacitorsare connected in parallel and Cs| is their effective capacity when

connected in series, then —— = n

Charging and Discharging of Capacitor in Series

As shown in the following figure (A) when switch S is closed,capacitor start charging. In this transient state potential differenceappears across capacitor as well as across resistor. When capacitorgets fully charged the entire potential difference appeared across thecapacitor and nothing is left for the resistor. [Shown in figure (B)]

I

* — v' i

*

(A)

RLZ AWU14V¥¥W

>< V *

• l l

s ^fTransient state

Fig. 18.100(i) Charging : In transient

capacitor at any instant Q

difference across the capacitor at

(B) Steady state

state of charging charge on the

( -1= Q0 1 - eRC and potential

any instant V = V0 1 - e RC

(Here Q and V are the instantaneous values of charge andpotential difference while maximum charge on capacitor is

Qo = CV0)

(ii) Discharging : After the completion of charging, if batteryis removed capacitor starts discharging. In transient state charge on

the capacitor at any instant Q = Q0e~' and potential difference

cross the capacitor at any instant V = V0e ~' 'R

Qc

Q!

0

= Q0(l-rwc)

QoQt

0 I

Charge on the capacitor increases Charge on the capacitor decreaseswith time during charging with time during discharging

Fig. 18.101

(iii) Time constant (7) : The quantity RC is called the timeconstant as it has the dimension of time during charging if

t = T = RC, Q = Q0(l-e-1) = 0.63Q0= 63% of Q0 (- = 0.37)e

or during discharging it is defined as the time during which chargeon a capacitor falls to 0.37 times (37%) of the initial charge on thecapacitor.

Kirchhoff's Law for Capacitor Circuits

According to Kirchhoff s junction law ]Tq = 0 and Kirchhoff s

second law (Loop law) states that in a close loop of an electric

circuit 7 — =*-c

Use following sign convention while solving the problems.

E , E ,

-E + E.

AV = - q/C AV = + q/C

Fig. 18.102

When an arrangement of capacitors cannot be simplified bythe method of successive reduction, then we need to apply theKirchhoff s laws to solve the circuit.

BJSS After earthing a positively charged conductor electrons flowfrom earth to conductor and if a negatively charged conductor isearthed then electrons flows from conductor to earth.

jeS When a charged spherical conductor is placed inside ahollow insulated conductor and connected through a fineconducting wire the charge wiil be completely transferred fromthe inner conductor to the oute • conductor.

£S If X-rays are incident onionisation of air by X-rays the

and hence its leaves will collap

jeS Lightening-rod arresters are made up of conductors withone of their ends earthed while the other sharp, and protects abuilding from lightening either oy neutralising or conducting thecharge of the cloud to the ground.

£5 With rise in temperature dielectric constant of liquid decreases.

a charged electroscope, due toelectroscope will get dischargedse. However, if the electroscope

is evacuated. X-rays will cause photoelectric effect with gold andso the leaves will further diverge if it is positively charged (or

uncharged) and will converge iflit is negatively charged.

jeS Two point charges separated by a distance r in vacuum anda force F acting between them.

To maintain the force as before

to be changed to ryK . This

on their surfaces will be — = - P- =

After filling a dielectric mediumhaving dielectric constant K completely between the charges,force between them decreases.

separation between them has

distance known as effective air separation.

jeS No point charge produces <;lectric field at it's own position.

eS The electric field on the surface of a conductor is directly

proportional to the surface chargs density at that point i.e, £ «= a

jeS Two charged spheres having radii rj and r2 , charge

densities ol and a2 respectively, then the ratio of electric field

r~

eS In air, if intensity of el

3 x!06N/C, air ionizes.

Bctric field exceeds the value

help of an insulated thread. If a

A small ball is suspended in a uniform electric field with thehigh energy X-ray beam falls on

the ball, X-rays knock out elections from the ball so the ball ispositively charged and therefqre the ball is deflected in thedirection of electric field.

X-Ray

F=QE

Electrostatics 977

jeZ Electric field is always directed from higher potential tolower potential.

& A positive charge if left free in electric field always movesfrom higher potential to lower potential while a negative chargemoves from lower potential to higher potential.

J& An electric potential can exist at a point in a region wherethe electric field is zero and it's vice versa.

jeS It is a common misconception that the path traced by apositive test charge is a field line but actually the path traced bya unit positive test charge represents a field line only when itmoves along a straight line.

eS An electric field is completely characterized by two physicalquantities Potential and Intensity. Force characteristic of thefield is intensity and work characteristic of the field is potential.

£$ For a short dipole, electric field intensity at a point on theaxial line is double the electric field intensity at a point on theequatorial line of electric dipole i.e. E^, = 2Eequatoria,

jeS It is interesting to note that dipole field E <*= — - decreases

much rapidly as compared to the field of a point charge

1

eS Franklin (i.e., e.s.u. of charge) is the smallest unit of chargewhile faraday is largest (1 Faraday = 96500 C).

jeS The e.s.u. of charge is also called stat coulomb or Franklin(Fr) and is related to e.m.u. of charge through the relation

emu of charge = 3xloioesu of charge

xS Recently it has been discovered that elementary particlessuch as proton or neutron are composed of quarks having

charge (±l/3)e and (±2/3)e. However, as quarks do not

exist in free state, the quanta of charge is still e.

& Inducting body neither gains nor loses charge.

JeS Dielectric constant of an insulator can not be °°

gS For metals in electrostatics K = °° and so Q' = - Q; i.e. in

metals induced charge is equal and opposite to inducing charge.

jsS A truck carrying explosives has a metal chain touching theground, to conduct away the charge produced by friction.

jeS Coulombs law is valid at a distance greater than 10~15m.

jeS Ratio of gravitational force and electrostatic force between

(i) Two electrons is Ifr43/!. (ii) Two protons is lO"36/!

(iii) One proton and one electron 10"39/!.

MS Decreasing order to fundamental forces

^Nuclear > ^Electromagnetic > MVeofc > ^Gravitational

978 Electrostatics

eS At the centre of the line joining two equal and opposite

charge V = 0 but E * 0.

jeS At the centre of the line joining two equal and similarcharge V * 0, E = 0 .

SS Electric field intensity an<jl electric potential due to a pointcharge q, at a distance t, + £J where ^ is thickness of mediumof dielectric constant K, an<[i t2 is thickness of medium ofdielectric constant K2 are :

l Q£ = - ; V = Q4;te

e$ If an electron (charge ej and mass m) is moving on acircular path of radius r aboutia positively charge infinitely long

linear charge, (charge density |i) then the velocity of electron in

dynamic equilibrium will be v j=

g$ A metal plate is charged uniformly with a surface chargedensity o. An electron of energy IV is fired towards the chargedmetal plate from a distance d, then for no collision of electron

with plate d = —-

£$ It is a very common misconception that a capacitor storescharge but actually a capacitor stores electric energy in theelectrostatic field between the plates.

jeS Two plates of unequal ar^a can also form a capacitor, buteffective overlapping area is considered.

I'M

K-d-

jeS Capacitance of a parallel'plate capacitor doesn't dependsupon the charge given, potential raised or nature of metals andthickness of plates.

MS The distance between the plates is kept small to avoidfringing or edge effect (non-Uniformity of the field) at theboundaries of the plates.

JtS Spherical conductor is equivalent to a spherical capacitorwith it's outer sphere of infinite radius.

j*f A spherical capacitor behaves as a parallel plate capacitor ifits spherical surfaces have large radii and are close to eachother.

jgS The intensity of electric field between the plates of a parallel

plate capacitor (E = O/£Q) does not depend upon the distancebetween them.

& The plates of a parallel plate capacitor are being movedaway with some velocity. If the plete separation at any instant of

time is 'd' then the rate of change of capacitance with time is

proportional to —.

Jg$ Radial and non-uniform electric field exists between thespherical surfaces of spherical capacitor.

fS Two large conducting plates X and Y kept close to each

other. The plate X is given a charge Qj while plate Y is given a

charge Q2(Qi > Q2), the distribution of charge on the four faces

a, b, c, d will be as shown in the following figure.

^t I J\t 2 i •X

I +Q2

V

2

Oi-Q 2Q+Q,

eS When dielectric is partially filled between the plates of aparallel plate capacitor then it's capacitance increases butpotential difference decreases. To maintain the capacitance andpotential difference of capacitor as before separation between

the plates has to be increased say by d' . In such case

K -t-d

jeS In series combination equivalent capacitance is alwayslesser than that of either of the individual capacitors. In parallel

combination, equivalent capacitance is always greater than themaximum capacitance of either capacitor in network.

MS If n identical capacitors are connected in parallel which arecharged to a potential V. If these are separated and connected inseries then potential difference of combination will be nV.

MS Two capacitors of capacitances Cl and C2 are charged topotential of Vj and V2 respectively. After disconnecting frombatteries they are again connected to each other with reversepolarity i.e., positive plate of a capacitor connected to negative

plate of other. Then common potential is given by

v = Qi-Q2 = cyi-c2v2Q + C, Q + C2

2.

3.

5.

6.

7.

8.

Objective Questions

(a) Ampere's law(c) Faraday's law

Charge and! Coulomb's Law

The law, governing th? force between electric charges isknown as [CPMT 1972; MP PMT 2004]

(b) Ohm's law(d) Coulomb's law

When the distance between the charged particles is halved,the force between them becomes [MNR 1986](a) One-fourth (b) Half(c) Double (d) Four timesThere are two charges 4-1 //C and +5 //C respectively.

The ratio of the forces acting on them will be [CPMT 1979](a) 1:5 (b) 1:1(c) 5:1 (d) 1:25Under the influence of ti\ Coulomb field of charge +Q, acharge -q is moving around it in an elliptical orbit. Find outthe correct statement(s) [IIT-JEE 2009](a) The angular momentum of the charge -q is constant(b) The linear momentum of the charge -q is constant(c) The angular velocity of the charge -q is constant(d) The linear speed of the charge -q is constant

Three concentric metallic spherical shells of radii R, 2R, 3R,are given charges Q1,Q2\Q3. respectively. It is found that

the surface charge densities on the outer surfaces of the shellsare equal. Then, the ratio of the charges given to the shells,Qi : Q2 : Q3 . is [IIT-JEE 2009]

(a) 1 : 2 : 3 (b) 1 : 3 : 5(c) 1 : 4 : 9 (d) 1 : 8 : 18

The ratio of the forces between two small spheres withconstant charge (a) in air (b) in a medium of dielectric

constant K is [MNR 1998](a) 1 : K (b) K : 1

(c) 1:K2 (d) K2 : lA soap bubble is given a nejgative charge, then its radius

[MNpfl988; CPMT 1997; RPMT 1997;DCE 2000; BVP 2003]

(a) Decreases(b) Increases(c) Remains unchanged(d) Nothing can be predicted as information is insufficientFour charges are arranged at the corners of a squareABCD , as shown in the adjoining figure. The force on thecharge kept at the centre O Is [NCERT 1983; BHU 1999]

-D

(a) Zero

(c) Along the diagonal BD

+ 2q

(b) Along the diagonal AC

(d) Perpendicular to side AB

Electrostatics 979

A charge Q is placed at each of the opposite corners of asquare. A charge q is placed at each of the other twocorners. If the net electrical force on Q is zero, then Q/qequals [AIEEE 2009; Similar MP PET 2008]

-2V2"(a)

(c)

(b) -1

10. A body can be negatively charged by

[CPMT 1972; AHMS 1998](a) Giving excess of electrons to it

(b) Removing some electrons from it

(c) Giving some protons to it

(d) Removing some neutrons from it

11. The charge q is projected into a uniform electric field E,work done when it moves a distance Y is [Orissa JEE 2009]

a) qEY

qE

(b)

(c)

12. Energy associated with a moving charge is due to a

[Orissa JEE 2008]

(a) Electric field

(b) Magnetic field

(c) Both electric field and magnetic field

(d) None of these

13. A total charge Q is broken in two parts Qj and Q2 and

they are placed at a distance R from each other. Themaximum force of repulsion between them will occur, when

[MP PET 1990]

(a) Q 9 = — , Q i = Q - — (b) Q? = — , Q, =Q- —v2 R,vi ^ R ^2 4 > ^ j 3

(c) - Q O - 3Q-j.Qi — (d)2 ' 2

14. Two identical conducting spheres carrying different chargesattract each other with a force F when placed in air mediumat a distance 'd' apart. The spheres are brought into contactand then taken to their original positions. Now the twospheres repel each other with a force whose magnitude isequal to that of the initial attractive force. The ratio betweeninitial charges on the spheres is [Kerala PET 2008]

(a) -(3 + V8)only (b) -3 + V8only

(c) -(3 + V8)or(-3+V8) (d) +V3

(e) -V815. In nature, the electric charge of any system is always equal

to [VITEEE 2008]

(a) Half integral multiple of the least amount of charge

(b) Zero

(c) Square of the least amount of charge

(d) Integral multiple of the least amount of charge

17.

18.

19.

20.

21.

22.

980 ElectrostaticsTwo small spheres each having the charge +Q aresuspended by insulating threads of length L from a hook.This arrangement is taken in space where there is nogravitational effect, them the angle between the twosuspensions and the tension in each will be [I1T 1986]

(a) 180°, Q2

o (2L)2

1 Q2(c) 180°,4;z£0 2L2

A solid sphere of radius

p = — is enclosed by a

(b)

(d)

an

90°^\J ,

ian°

id volume

Q2

, L2

Q2

• L2

charge density

hollow sphere of radius R2 with

negative surface charge density a, such that the totalcharge in the system is zero. pQ is a positive constant and r

is the distance from the! centre of the sphere. The ratiois [VITEEE2008]

a

Po(b)

(d)

A solid spherical conductor of radius R has a spherical cavityof radius a (a < R) at its Centre. A charge +Q is kept at the

center. The charge at the inner surface, outer and at aposition r ( a < r <R) are respectively [VITEEE 2008]

(a) + Q.-Q.O0,-Q,0

(b) -Q, + Q,0

(d) +Q,0,0

The surface charge densii/ (in C / m2 ) of the earth is about[DUMET 2009]

(a)

(c)

1C 9

109

(b) -109

(d) -HT9

There are two metallic spheres of same radii but one is solidand the other is hollow, then [KCET 1994; BHU 1999](a) Solid sphere can be given more charge(b) Hollow sphere can be given more charge(c) They can be charged equally (maximum)(d) None of the aboveOne of the following is n0t a property of field lines

[DUMET 2009](a) Field lines are continuous curves without any breaks(b) Two field lines cannot cross each other(c) Field lines start at positive charge and end at negative

charges(d) They form closed loopsThree equal charges are placed on the three corners of asquare. If the force between ql and q2 is F12 and that

pbetween qj and q3 is ff13 , the ratio of magnitudes — - is

i~n

(a) 1/2

(c) 1/V2

[MP PET 1993]

(b) 2

(d) V2

23. ABC is a right angled triangle in which AB = 3cm and

BC = 4cm. And Z. ABC = Jti2. The three charges

+15, +12 and -20e.s.u. are placed respectively on A , B

and C . The force acting on B is(a) 125 dynes (b) 35 dynes

(c) 25 dynes (d) Zero

24. Two small spherical balls each carrying a charge Q=lQfjC(10 micro-coulomb) are suspended by two insulatingthreads of equal lengths 1m each, from a point fixed in theceiling. It is found that in equilibrium threads are separatedby an angle 60° between them, as shown in the figure. Whatis the tension in the threads (Given:

= 9xl09Nm/C2 ) [MP PET 2001; Pb. PET 2003]

(a) 18 N

(b) 1.8 N

(c) 0.18 N

(d) None of the above

25. Two charges q^ and q2 are placed in vacuum at a distance

d and the force acting between them is F . If a medium ofdielectric constant 4 is introduced between them, the forcenow will be [MP PMT 1994](a) 4F (b) 2F

26. Force of attraction between two point charges Q and - Qseparated by d metre is Fe . When these charges are placed

on two identical spheres of radius R = 0.3 d whose centres

are d metre apart, the force of attraction between them is

[AIIMS 1995](a) Greater than Fe (b) Equal to Fe

(c) Less than Fe (d) None of these

27. Consider a neutral conducting sphere. A positive pointcharge is placed outside the sphere. The net charge on thesphere is then [1IT-JEE 2007](a) Negative and distributed uniformly over the surface of

the sphere(b) Negative and appears only at the point on the sphere

closest to the point charge(c) Negative and distributed non-uniformly over the entire

surface of the sphere(d) Zero

28. A force F acts between sodium and chlorine ions of salt(sodium chloride) when put 1cm apart in air. The

permittivity of air and dielectric constant of water are £0

and K respectively. When a piece of salt is put in waterelectrical force acting between sodium and chlorine ions1cm apart is [MP PET 1995]

">*(c)

K£O

(b) ™

(d)K

33.

Two identical charges repel each other with a force equal to10 mg wt when they are 0.6 m apart in air. (<j=10ms~2). Thevalue of each charge is [Karnataka CET 2007](a) 2mC (b) 2xlO-7C(c) 2nC (d) 2fjC

30. The value of electric permittivity of free space is[MP PET 1996; RPET 2001]

(a) 9xl09NC2 /m2 (b) 8.85xlO"12Nm2/C2sec

(c) 8.85xlO-12C2/Nrf72 (d) 9xl09C2/Nm2

31. Two similar spheres hav ng +q and -q charge are kept at

a certain distance. F fdrce acts between the two. If in themiddle of two spheres, another similar sphere having +q

charge is kept, then it experience a force in magnitude anddirection as [MP PET 1996](a) Zero having no direction (b) 8F towards +q charge

rge (d) 4F towards +q charge

o two parts of q and Q - q . If the

n them when they are separated is

of — should be

38.

(c) 8F towards -q che

32. A charge Q is divided in

coulomb repulsion betwei

to be maximum, the ratio

[MP PET 1997; Kerala PET 2011](a) 2 (b) 1/2(c) 4 (d) 1/4Number of electrons in or^e coulomb of charge will be

[MP PMT/PET }998; Pb. PMT 1999; AIIMS 1999;RPET 2001; S milar RPET 2004; WB-JEE 2009]

(b) 6.25 xlO18

(d) 9xlOn

dielectric medium of constant k ,attraction between two charges

[CBSE PMT 1999](b) Remains unchanged

(d) Increases k'1 timessilk is used to charge a gold leaf'es are observed to diverge. The

(a) 5.46 xlO29

(c) 1.6xlO+19

34. When air is replaced by athe maximum force ofseparated by a distance(a) Decreases k times

(c) Increases k times35. A glass rod rubbed with

electroscope and the leaelectroscope thus charged is exposed to X-rays for a shortperiod. Then [AMU 1995](a) The divergence of leaves will not be affected(b) The leaves will diverge further(c) The leaves will collapse(d) The leaves will melt

36. One metallic sphere A is given positive charge whereasanother identical metallic s|phere B of exactly same mass asof A is given equal amourit of negative charge. Then

[AMIU 1995; RPET 2000; CPMT 2000](a) Mass of A and mass of B still remain equal(b) Mass of A increases(c) Mass of B decreases(d) Mass of B increases

37. The force between two charges 0.06m apart is 5N. If

each charge is moved towards the other by 0.01m, then

the force between them wil

(a)

(c)

7.20 N

22.50 N

become [SCRA 1994](b)

(d)

11.25N

45.00 N

39.

40.

41.

42.

43.

44.

45.

46.

(b) F

Two charged spheres separated at a distance d exert a forceFon each other. If they are immersed in a liquid ofdielectric constant 2, then what is the force (if all conditionsare same) [AIIMS 1997; MH CET 2003]

-I(c) 2F (d) 4FTwo point charges +3//C and +8//C repel each other with

a force of 40/V . If a charge of -5//C is added to each of

them, then the force between them will become[SCRA 1998; JIPMER 2000;

Similar Orissa JEE 2008; DPMT 2009]

(a) -ION (b) +10N(c) +20N (d) -20N

When 1019 electrons are removed from a neutral metalplate, the electric charge on it is

[Manipal MEE 1995; Karnataka CET (Engg./Med.) 1999]

(a) -1.6C (b) + 1.6 C(c) 10+19C (d) 10-19CElectric charges of IfjC, - 1//C and 2//C are placed in air

at the corners A, B and C respectively of an equilateraltriangle ABC having length of each side 10 cm. Theresultant force on the charge at C is [EAMCET (Engg.) 2000](a) 0.9 N(c) 2.7 NCharge on a -particle is

(a) 4.8xHT19C

(c) 3.2xlO"19C

(b) 1.8N(d) 3.6 N

[MH CET 2000]

(b) 1.6xlO~19C

(d) 6.4xlO~19CTwo small conducting spheres of equal radius have charges+10//C and -20//C respectively and placed at a distance

R from each other experience force Fj. If they are brought

in contact and separated to the same distance, theyexperience force F2 . The ratio of Fj to F2 is

[MP PMT 2001; Orissa JEE 2011; Similar J & K CET 2006;K?mataka CET 2008]

(a) 1 : 8 (b) - 8 : 1(c) 1:2 (d) -2:1

Two charges each equal to 2//C are 0.5m apart. If both ofthem exist inside vacuum, then the force between them is

[CPMT 2001; Similar CPMT 1977; DPMT 1999]

(a) 1.89N (b) 2.44 N

(c) 0.144JV (d) 3.144NTwo charges are at a distance 'd' apart. If a copper plate

(conducting medium) of thickness - - is placed between

them, the effective force will be[UPSEAT 2001; J & K CET 2005]

(a) 2F (b) F / 2

(c) 0 (d) A/2F

Two electrons are separated by a distance of 1A. What is thecoulomb force between them [MH CET 2002]

(a) 2.3xHT8N (b) 4.6xlO~8N

(c) l.SxlO^N (d) None of these

48.

49.

50.

51.

52.

982 Electrostatics

Two copper balls, each weighting lOg are kept in air 10 cm

apart. If one electron from every 106 atoms is transferredfrom one ball to the other, ithe coulomb force between themis (atomic weight of copper is 63.5) [KCET 2002]

(a) 2.0xl010N (b) 2.0xl04N

(c) 2.0xl08N (d) 2.0xl06NA solid conducting sphere of radius a has a net positivecharge 2Q. A conducting spherical shell of inner radius band outer radius c is concentric with the solid sphere andhas a net charge - Q. The surface charge density on theinner and outer surfaces of 'the spherical shell will be

[AMU 2002]

(b) -

2Q Q

4^b2 ' 4;rc2

_Q Q_4^2 '4^c2

Q(c) 0,.Hm"

(d) None of the aboveThree charges each of magnitude q are placed at the cornersof an equilateral triangle, the electrostatic force on thecharge placed at the center is (each side of triangle is L)

[DPMT 2002]

1_

~ L2

,2

(a) Zero

3q2

(b) ^^

12 0 Lf-Two charges placed in air repel each other by a force of

10 N . When oil is introduced between the charges, the

force becomes 2.5 x 10~5N . The dielectric constant of oil is[MP PET 2003]

2.5 (b) 0.252.0 (d) 4.0

Three charges are placed at the vertices of an equilateraltriangle of side 'a' as shown in the following figure. Theforce experienced by the charge placed at the vertex A in adirection normal to BC is A [AIIMS 2003]

(a)(c)

(a) Q2 /

(b) -Q2

(c) Zero

(d) Q2

+ Q

I+QB a c

Two particle of equal mass m and charge q are placed at adistance of 16 cm. They do not experience any force. The

value of — ism

(c)

[MP PET 2003]

53. When a glass rod is rubbed(a) Gains electrons from si(b) Gives electrons to silk(c) Gains protons from silk(d) Gives protons to silk

(d)

with silk, it [MP PET 2003]

54. An electron is moving around the nucleus of a hydrogen

atom in a circular orbit of radius r. The coulomb force F1

55.

56.

57.

58.

59.

60.

61.

between the two is (Where K = ) [CBSE PMT 2003]

a -J

(c) -K^-i

(b) K^-i

(d) K^-i

A body has - 80 micro coulomb of charge. Number ofadditional electrons in it will be [MP PMT 2003]

(a) 8xlO~5 (b) SOxHT17

(c) 5xl014 (d) 1.28 xlO'17

Two point charges placed at a certain distance r in air exerta force F on each other. Then the distance r' at which thesecharges will exert the same force in a medium of dielectricconstant k is given by [EAMCET 1990; MP PMT 2001]

(a) r (b) r/k

(c) r /Vfc (d) rVfc

Dielectric constant for metal is [MP PMT/PET 1998]

(a) Zero (b) Infinite

(c) 1 (d) Greater than 1

A charge of Q coulomb is placed on a solid piece of metal ofirregular shape. The charge will distribute itself

[MP PMT 1991]

(a) Uniformly in the metal object

(b) Uniformly on the surface of the object

(c) Such that the potential energy of the system isminimised

(d) Such that the total heat loss is minimised

Five balls numbered 1 to 5 are suspended using separatethreads. Pairs (1, 2), (2, 4) and (4, 1} show electrostaticattraction, while pair (2, 3) and (4, 5) show repulsion.Therefore ball 1 must be [NCERT 1980; MP PMT 2003]

(a) Positively charged (b) Negatively charged

(c) Neutral (d) Made of metal

Equal charges q are placed at the four corners A, B, C, D

of a square of length a . The magnitude of the force on thecharge at B will be [MP PMT 1994; DPMT 2001]

(b)

(d) 2 +

Two identical conductors of copper and aluminium areplaced in an identical electric fields. The magnitude ofinduced charge in the aluminium will be [AIIMS 1999]

(a) Zero

(b) Greater than in copper

(c) Equal to that in copper

(d) Less than in copper

67.

Two spherical conductors B and C having equal radii andcarrying equal charges in them repel each other with a forceF when kept apart at some distance. A third sphericalconductor having same j radius as that of B but uncharged isbrought in contact witrj B, then brought in contact with Cand finally removed a|vay from both. The new force ofrepulsion between B an< C is

(a)(c)

F/4F/8

63. When a body is earthflow into the body. This

(a) Unchanged(c) Charged negatively

[AIEEE 2004]

(b)

(d)

3F/4

3F/8

:onnected, electrons from the earthmeans the body is [KCET 2004]

(b) Charged positively(d) An insulator

64. The charges on two spheres are +7//C and - 5//Crespectively. They expedience a force F. If each of them isgiven and additional charge of - 2//C, the new force ofattraction will be [RPET 2002](a) F (b) F/2

(c) F/V3 (d) 2F

65. The ratio of electrostatic and gravitational forces actingbetween electron and proton separated by a distance

5xlCrnm, will be (Charge on electron = 1.6 x 10~19 C, mass

of electron = 9.1 x lO"31 tfg. mass of proton = 1.6xl(T27/cg,

) [RPET 1997; Pb. PMT 2003]

(b) 2.36 xlO40

(d) 2.34xlO42

G = 6.7xlO-n/Vm2/fcg

(a) 2.36 xlO39

(c) 2.34 xlO41

66. Two identical spheres c;

respectively are kept in

trying charges -9//C and 5//C

contact and then separated fromeach other. Point out trueach sphere

(a) 1.25 xlO13 electrons

e statement from the following. In[Kerala PMT 2007]

are in deficit

(b) 1.25xl013 electrons are in excess

(c) 2.15 x 1013 electrons fire in excess

(d) 2.15x 1013 electrons W in deficitTwo equally charged, identical metal spheres A and B repeleach other with a force 'Fdistance V between themsphere C is brought in con

net electric force on C is(a) F(c) F/2

The spheres are kept fixed with aA third identical, but uncharged

act with A and then placed at themid-point of the line joining A and B. The magnitude of the

[UPSEAT 2004; DCE 2005](b) 3F/4(d) F/4

68. Two charges of equal magnitudes and at a distance r exert aforce F on each other. If thbetween them is doubled,charge is(a) F/8(c) 4F

69. An infinite number of chcplaced on the x-axis with ca charge of 1 C is kept aforce acting on 1 C charge

(a) 9000 N(c) 240007V

charges are halved and distancelen the new force acting on each

[DCE 2004](b) F /4(d) F/16

rges, each of charge 1 //C, are-ordinates x = 1, 2, 4, 8, ....«>. Ifthe origin, then what is the net

[DCE 2004](b) 12000 N(d) 36000 N

70. The top of the atmosphere is at about 400 kV with respect tothe surface of the earth, corresponding to an electric fieldthat decreases with altitude. Near the surface of the earth,the field is about 100 Vm~l. Still, we do not get an electricshock as we step out of our house into the open housebecause (assume the house to be a steel cage so that there isno field inside) [Kamataka CET 2006]

(a) There is a potential difference between our body andthe ground

(b) 100 Vnr1 is not a high electric field so that we do notfeel the shock

(c) Our body and the ground forms an Equipotentialsurface

(d) The atmosphere is not a conductor

71. Four metal conductors having different shapes

1. A sphere 2. Cylindrical

3. Pear 3. Lightning conductor

are mounted on insulating stands and charged. The onewhich is best suited to retain the charges for a longer time is

[KCET 2005]

(a) 1 (b) 2

(c) 3 (d) 4

72. Identify the wrong statement in the following. Coulomb's lawcorrectly describes the electric force that (KCET 2005]

(a) Binds the electrons of an atom to its nucleus

(b) Binds the protons and neutrons in the nucleus of anatom

(c) Binds atoms together to form molecules

(d) Binds atoms and molecules together to form solids

73. Which of the following will represent coulomb's law

[BCECE 2006]

(a)

(c)

(b)

(d)

74. A comb run through one's dry hair attracts small bits ofpaper. This is due to [Kamataka CET 2006]

(a) Comb is a good conductor

(b) Paper is a good conductor

(c) The atoms in the paper get polarised by the chargedcomb

(d) The comb possesses magnetic properties

75. Two positive ions, each carrying a charge q, are separatedby a distance d. If F is the force of repulsion between theions, the number of electrons missing from each ion will be(e being the charge on an electron) [CBSE PMT 2010]

&-

Fe2 (d)

984 Electrostatics

78.

79.

80.

Two charges +6//C and +15//C are placed along the

x-axis at x = 0 and x = 2 m respectively A negative chargeis placed between them such that the resultant force on it iszero. The negative charge is placed at [Orissa JEE 2010]

(a) x = 0.775m

(b) x = 1.2m

(c) x = 0.5m

(d) Position depends on the amount of charge

77. Two protons are a distance

The forces acting on them a

of 1x10 10 cm from each other.

re. [Orissa JEE 2010]

(a) Nuclear force and coulomb force

(b) Nuclear force and gravitational force

(c) Coulomb force and gravitational force

(d) Nuclear, coulomb and gravitational force

Two identical conducting balls A and B have positive charges q,and q2 respectively. But q1 =4 qz. The balls are brought together

so that they touch each other and then kept in their originalpositions. The force between them is [Kamataka CET 2010]

(a) Less than that before the balls touched

(b) Greater than that befote the balls touched

(c) Same as that before thje balls touched

(d) Zero

Two small spheres of masses M, and M2 are suspended byweightless insulating thread$ of lengths L; and L2. The spherescarry charges Qj and Q2 respectively. The spheres aresuspended such that they are in level with one another and thethreads are inclined to the vertical at angles of 0l and 02 &*

shown. Which one of the following conditions is essential, if

#! -0 [Kamataka CET 2010]

(a)

A ball with charge -50 e is placed at the centre of a hollowspherical shell which has a net charge of -50 e. What is thecharge on the shell's outer 'surface [DUMET 2010]

-50e

-lOOe-.10

(b) Zero

(d) +100e

81. If 10 electrons are acquired by a body every second, thetime required for the body

(a) Two hours

(c) Two years

to get a total charge of 1 C will be

[DUMET 2010]

(b) Two days

(d) 20 years

82. Two charged spherical conductors of radii Rj and R2 are

connected by a wire. Then the ratio of surface chargedensities of the spheres av I a? is [Kerala PET 2010]

83.

84.

85.

(a)R

(b) 4^

*'f

A conductor has been given a charge -3xlO~7C bytransferring electron. Mass increase (in kg) of the conductorand the number of electrons added to the conductor arerespectively [AMU (Engg.) 2010]

(a) 2xKT16 and 2xl031 (b) 5xlO~31 and 5xl019

(c) 3xlO~19 and 9xl016 (d) 2xKT18 and 2xl012

A ring of radius r carries a charge Q uniformly distributedover its length. A charge q is placed at its centre will

experience a force equal to [Orissa JEE 2010]

(b) -

(c) Zero (d) None of theseFour point charges -Q, -q, 2q and 2Q are placed, one ateach corner of the square. The relation between Q and q forwhich the potential at the centre of the square is zero is

[CBSE PMT (Pre.) 2012]

Q=-q

(c) Q=q

(b)

(d)

Electric Field and Potential

A charge q is placed at the centre of the line joining twoequal charges Q. The system of the three charges will be inequilibrium, if q is equal to[IIT 1987; CBSE PMT 1995; Bihar MEE 1995; CPMT 1999;

MP PET 1999; MP PMT 1999, 2000; RPET 1999;KCET 2001; AIEEE 2002; AFMC 2002;

Kerala PMT 2004; J & K CET 2004]

«-f

(c,

N-aWl +f

QLet P(r) = —j-r be the charge density distribution for a

solid sphere of radius R and total charge Q. For a point 'p'inside the sphere at distance rjfrom the centre of the

sphere, the magnitude of electric field is [AIEEE 2009]

Q(a) 0

Qr,2

4;re

(b)

(d) Qr?3;re0 R4

4.

Electrostatics J?85

10.

Two small spheres each carrying a charge q are placed rmetre apart. If one of the sphere is taken around the otherone in a circular path of radius r, the work done will beequal to [CPMT 1975, 91, 2001; NCERT 1980, 83;EAMCET 1994; MP PET 1995; MNR 1998; Pb. PMT 2000]

(a) Force between them x r

(b) Force between them x 2nr

(c) Force between them I2nr

(d) Zero

Two points P and Q are meiintained at the potentials of 10 Vand -4V, respectively. The work done in moving 100

[AIEEE 2009]

10

electrons from P to Q is

(a) -9.60xKT17J

(c) -2.24xlO"16J

5. Two charged spheres o:connected by a thin wire. 1

(b) 9.60xlO~17J

(d) 2.24xHT16J

radii 10 cm and 15 cm areo charge will flow, if they have

[CPMT 1975; MP PET 1991]

(a) The same charge on efech

(b) The same potential

(c) The same energy

(d) The same field on thei|r surfaces

spherical shell of uniform surface1982; MP PET 1994; RPET 2000]

6. The electric field inside acharge density is [CPM1 :

(a) Zero

(b) Constant, less than ze:

(c) Directly proportional to the distance from the centre

(d) None of the above

7. The electric potential V at any point O (x, y, z all in metres)in space is given by V=ftx2 volt. The electric field at thepoint (1m, 0, 2m) in uo/t/rfierre is [HT 1992; RPET 1999;

MP PMT 2001; Similar Kamataka CET 2009]

(a) 8 along negative X-axis (b) 8 along positive X-axis

(c) 16 along negative X-.ixis (d) 16 along positive Z-axis

8. A hollow metal sphere ofpotential on its surface is

radius 5 cm is charged so that the10 V. The potential at the centre

of the sphere is [HT 1983; MNR 1990; MP PET/PMT 2000;DPMT 2004; Similar MP PMT 2009]

(a) 0V

(b) 10 V

(c) Same as at point 5 citn away from the surface

(d) Same as at point 25 Cm away from the surface

9. If a unit positive charge s taken from one point to anotherover an equipotential suriace, then

[KCET 1994; CPMT 1997; CBSE PMT 2000; BCECE 2004;Similar WB-JEE 2009]

(a)

(b)

(c)(d)

Work is done on the

Work is done by the

charge

charge

Work done is constant

No work is done

Electric lines of force abojut negative point charge are[MP PMT 1987]

(a) Circular, anticlockwise (b) Circular, clockwise

(c) Radial, inward (d) Radial, outward

11. Charges of + — xlO"9C are placed at each of the four

corners of a square of side 8cm. The potential at theintersection of the diagonals is [BIT 1993]

(a) 150V2uo/t (b) 1500^/2 volt

15.

16.

c) 900V2uo/t (d) 9QOuolt

12. A uniform electric field having a magnitude £0 and directionalong the positive X-axis exists. If the potential V is zero atx=0, then its value at X= +x will be [MP PMT 1987]

(a) V ( x )=+xE0 (b) Vx=-xE0

(c) V x = + x 2 E 0 (d) V x = - x 2 E 0

13. Three charges 2q, ~q, -q are located at the vertices of anequilateral triangle. At the centre of the triangle

[MP PET 1985; J & K CET 2004; Kerala PET 2009]

(a) The field is zero but potential is non-zero(b) The field is non-zero but potential is zero(c) Both field and potential are zero(d) Both field and potential are non-zero

14. Figure shows the electric lines of force emerging from acharged body. If the electric field at A and B are EA and EB

respectively and if the displacement between A and B is rthen [CPMT 1986, 88]

(a) E A >E B (b) E A < E B

(c) E A =^ (d) EA=^fr r

ABC is an equilateral triangle. Charges +q are placed ateach corner. The electric intensity at O will be

[CPMT 1985; AIEEE 2002]

(b) 1

(c) Zero

IA\)O

B

•' ->

C

In the electric field of a point charge q, a certain charge iscarried from point A to B, C, D and E. Then the work done

[NCERT 1980]

(a) Is least along the path AB

(b) Is least along the path AD

(c) Is zero along all the paths AB,

AC, AD and AE

(d) Is least along AE

18.

19.

20.

21.

22.

23.

24.

986 Electrostatics

The magnitude of electric field intensity £ is such that, anelectron placed in it would experience an electrical forceequal to its weight is given by

[CPMT 1975, 80; AFMC 2001; BCECE 2003]

(a) mge

emg

(b) e

(d) -4i

Three concentric spherical shells have radii a, fa andc (a < b < c) and have Surface charge densities a, - a and a

respectively. If VA, VB and Vc denote the potentials of the

three shells, then, for c = a + b, we have [CBSE PMT 2009]

(a) VC=VA*VB (b) VC=VB*VA

(c) VC*VB*VA (d) VC=VB=VA

An electron and a proton are in a uniform electric field, theratio of their accelerations will be

[NCERT 1984; MP PET 2002](a) Zero(b) Unity(c) The ratio of the masses of proton and electron(d) The ratio of the masses of electron and protonTwo parallel plates have equal and opposite charge. Whenthe space between them is evacuated, the electric field

between the plates is 2xl05V/m . When the space is filled

with dielectric, the electric field becomes l x l0 5 V/m . Thedielectric constant of the jdielectric material [MP PET 1989](a) 1/2 (b) 1(c) 2 (d) 3The insulation property of air breciks down at £ = 3xl06

volt/metre. The maximum charge that can be given to asphere of diameter 5 m te approximately (in coulombs)

[MP PMT 1990]

(b) 2xl(T3

(d) 2xl(T5

(a) 2xlCT2

(c) 2x10-"The electric potential at a point (x, y, z) is given by

V = -x2y - xz3 + 4

The electric field E at th t point is

(a) £ = i (2xy + z3) + jx 2 +/c3 x z 2

[CBSE PMT 2009]

(b)

(d)

£ = / 2xy + j (x2 + y f ) + k (3xz - y2)

£ = j z3 + j xyz -i- k zp

E = i (2xy - z3) + j x,y2 + k 3z2x

Two spheres A and B of radius, 4cm and 6cm are givencharges of 80//C and 40//C respectively. If they are

connected by a fine wire, the amount of charge flowing fromone to the other is [MP PET 1991](a) 20//C from A to B (b) 16//C from A to B

(c) 32//C from B to A (d) 32//C from A to B

The mean free path of electrons in a metal is 4 x 1CT8 m . The

electric field which can give on an average 2 eV energy to an

electron in the metal will be in units of V/m [CBSE PMT 2009]

(a) 8xl07

(c) SxlCT11

(b) SxHT11

(d) 5xl07

25. If £ is the electric field intensity of an electrostatic field, thenthe electrostatic energy density is proportional to

[MP PMT 2003]

(a) £ (b) E2

(c) l/£2 (d) £3

26. The charge given to any conductor resides on its outersurface, because [MP PET 2009]

(a) The free charge tends to be in its minimum potentialenergy state

(b) The free charge tends to be in its minimum kineticenergy state

(c) The free charge tends to be in its maximum potentialenergy state

(d) The free charge tends to be in its maximum kineticenergy state

27. In identical mercury droplets charged to the same potentialV coalesce to form a single bigger drop. The potential ofnew drop will be [Kerala PET 2008; MP PET 2009]

29.

(a) (b) nV

(c) nV2 (d) nz/3V

28. An uncharged sphere of metal is placed in between twocharged plates as shown. The lines of force look like

[MP PMT 1985; KCET 2004]

+ + + + + + +

_ /

C D(a) A (b) B

(c) C (d) D

In figure + Q charge is located at one of the edge of the cube,then electric flux through cube due to + Q charge is

[MP PMT 2009]

(b)

(d)

+Q2e0

+Q8en

30. On rotating a point charge having a charge q around acharge Q in a circle of radius r. The work done will be

[CPMT 1990, 97; MP PET 1993, 2010, AIIMS 1997;

DCE 2003; KCET 2005; WB-JEE 2009; Kerala PMT 2011]

31.

33.

34.

36.

\vir

Q

Two parallel metal plates having charges + Q and -Q face

each other at a certain distance between them. If the platesare now dipped in kerojsene oil tank, the electric fieldbetween the plates will [CBSE PMT (Mains) 2010]

(a) Become zero

(c) Decrease

321. The number of electrons tp be put on a spherical conductorof radius O.lm to produc

just above its surface is

e an electric field of 0.036N/C

(a) 2.7 xlO5

(c) 2.5 xlO5

(b) Increase

(d) Remain same

MNR 1994; KCET (Engg.) 1999;

MH CET (Med.) 2001]

(b) 2.6 xlO5

(d) 2.4 xlO5

Two plates are 2cm apart, a potential difference of 10 volt

is applied between them, tie electric field between the platesis [MP PET 1994; DPMT 2002]

(a) 20 N/C (b) 500N/C

(c) 5N/C (d) 250 N/C

The intensity of the electric field required to keep a waterdrop of radius 10~5 cm just suspended in air when chargedwith one electron is approximately [MP PMT 1994]

(a) 260 volt/cm (b) 260 newton'coulomb

(c) 130 volt/cm (d) 130 newton'coulomb

(g=10 newton/kg, e=1.6>

35. Conduction electrons are c

a conducting plate. Whenthe electric field within the

(a) Is zero

(b) Depends upon E

(c) Depends upon E

(d) Depends upon the a

10-19 coulomb)

Imost uniformly distributed within

placed in an electrostatic field E ,plate [MP PMT 1994]

tomic number of the conductingelement

Three particles, each havirig a charge of 10 //C are placed atthe corners of an equilateral triangle of side 10 cm. Theelectrostatic potential energy of the system is (Given

= 9 x l 0 9 N - m 2 / C 2 ) [MP PMT 1994]

(b) Infinite

(d) 100 J

(a) Zero

(c) 27 J

37. The electric field near a conducting surface having a uniformsurface charge density cris given by

[MP PMT 1994; Gujarat CET 2007]

(a) — and is parallel to the surface

*7(b) — and is parallel to the surface

(c) — and is normal to the surface£o

(d) - and is normal to the surface£Q

38. There is an electric field E in X-direction. If the work doneon moving a charge 0.2 C through a distance of 2m along aline making an angle 60° with the X-axis is 4.0, what is thevalue of E [CBSE PMT 1995]

(a) V3N/C (b) 4 N / C

(c) 5 N / C (d) None of these

39. Four equal charges Q are placed at the four corners of asquare of each side is 'a'. Work done in removing a charge-Q from its centre to infinity is [AIIMS 1995]

V2Q2(a) 0

(c)V2Q2

(b)

(d) Q2

40. A particle A has charge +q and a particle B has charge +4qwith each of them having the same mass m. When allowedto fall from rest through the same electric potential

difference, the ratio of their speed — will become"B

[MNR 1991; BHU 1995; UPSEAT 2000; Pb. PET 2004]

(a) 2:1 (b) 1:2

(c) 1:4 (d) 4:1op

41. The electric field at a distance: — from the centre of a

charged conducting spherical shell of radius R is E. The

^electric field at a distance — from the centre of the sphere is

a) Zero

E

[CBSE PMT (Mains) 2010]

(b) E

(c)

42. Angle between equipotential surface and lines of force is

[MP PET 1995]

(a) Zero (b) 180°

(c) 90° (d) 45°

988 Electrostatics43. Below figures (1) and (2) represent lines of force. Which is

correct statement [MP PET 1995]

45.

46.

47.

48.

49.

(1)(a) Figure (1) represents magnetic lines of force(b) Figure (2) represents magnetic lines of force(c) Figure (1) represents electric lines of force(d) Both figure (1) and figure (2) represent magnetic lines

of force44. The unit of electric field is not equivalent to [MP PMT 1995]

(a) N/C (b) J/C

(c) V/m (d) J / C - m

A flat circular disc has a charge +Q uniformly distributed on

the disc. A charge +q if thrown with kinetic energy E

towards the disc along its normal axis. The charge q will

[MP PMT 1995](a) Hit the disc at the centre(b) Return back along its path after touching tne disc(c) Return back along its path without touching the disc(d) Any of the above thr^e situations is possible depending

on the magnitude of EAt a certain distance from a point charge the electric field is500V/m and the potential is 3000V. What is this

distance [MP PMT 1995; Pb. PMT 2001; AFMC 2001;RPMT 2005; J & K CET 2006]

(a) 6m (b) 12m

(c) 36m (d) 144m

The magnitude of electric field E in the annular region of acharged cylindrical capacitor [IIT 1996](a) Is same throughout(b) Is higher near the outer cylinder than near the inner

cylinder(c) Varies as 1 / r , where r is the distance from the axis

(d) Varies as I/ r 2 , where r is the distance from the axis

A metallic solid sphere is placed in a uniform electric field.The lines of force follow the path(s) shown in figure as

1 > y^ ?Ns > i [IIT 1996]9 / \, o

( \-rX

3 * \ /—> 3

4—*-" X 7 ~~*~ 4

(a)(c)

13

The distance between a proton and electron both having a

charge 1.6xlO~19cou/omb , of a hydrogen atom js

10"10 metre . The value of intensity of electric fieldproduced on electron due to proton will be

[MP PET 1996; Similar MP PET 19951]

(a) 2.304 xlO-1 0N/C (b) 14.4 V/m

(c) 16V/m (d) 1.44xlOnN/C

50.

51.

52.

53.

54.

What is the magnitude of a point charge due to which theelectric field 30cm away has the magnitude

2newton/coulomb [1/4^0 = 9xl0 9Nm 2 /C 2 ]

[MP PMT 1996, 2000; RPET 2001]

(a) 2xlO"ncou/omb (b) 3xlO"ncou/omfa

(c) 5xlO~ucou/omfa (d) 9xlO'ncou/omb

Two charge +q and -q are situated at a certain distance.

At the point exactly midway between them [Roorkee 2000]

(a) Electric field and potential both are zero

(b) Electric field is zero but potential is not zero

(c) Electric field is not zero but potential is zero

(d) Neither electric field nor potential is zero

Two charged spheres of radii /?j and R2 having equal

surface charge density. The ratio of their potential is

[Orissa JEE 2009]

(a) /?!/R2 (b) / ? 2 /Rj

( c ) ( R . / R z ) 2 ( d ) ( R 2 / R , ) 2

An a-particle of mass 6.4xlO~27fcg and charge

3.2xlO~19C is situated in a uniform electric field of

1.6xl05 VrrT1. The velocity of the particle at the end of

2 x 10~~ m path when it starts from rest is

[Kamataka CET 2009]

(a) 2V3xl05ms J (b) 8xl05ms"1

(c) 16xl05ms"1 (d) 4V2xl05ms~1

Consider a system of three charges — , — and - - placedO O O

at points A, B and C, respectively, as shown in the figure.Take O to be the centre of the circle of radius R and angleCAB = 60° [IIT-JEE 2008]

(a) The electric field at point O is - ! — directed along

the negative x-axis

(b) The Potential energy of the system is zero

(c) The magnitude of the force between the charges at C

and B is

(d) The potential at point O is — -

55.

56.

58.

59.

60.

A thin conducting ring oi radius R is given a charge +Q. The electric field at the centre O of the ring due tothe charge on the part AKB of the ring is E. The electricfield at the centre due tol the charge on the part ACDBof the ring is [CBSE PMT 2008](a) E along KO(c) SEalongKO

(b) 3 E along OK(d) E along OK

In Millikan's oil drop experiment an oil drop carrying acharge Q is held stationary by a potential difference 2400 V

between the plates. To tyeep a drop of half the radiusstationary the potential difference had to be made 600V .

What is the charge on the second drop [MP PET 1997]

(c) Q

57. A charge of 5C experien

(d)3Q2

:es a force of 5000 N when it is

kept in a uniform electiic field. What is the potentialdifference between two points separated by a distance of1cm [MP PET 1997]

(a) 10 V (b) 250V

(c) 1000 V (d) 2500V

Two insulated charged conducting spheres of radii 20cm

and 15cm respectively and having an equal charge of IOC

are connected by a ccpper wire and then they areseparated. Then [MP PET 1997](a) Both the spheres will have the same charge of IOC

(b) Surface charge densiy on the 20cm sphere will be

greater than that on ft e 15cm sphere

(c) Surface charge density on the 15cm sphere will be

greater than that on the 20cm sphere

(d) Surface charge density; on the two spheres will be equalEqual charges q are placed at the vertices A and B of anequilateral triangle ABCi of side a . The magnitude ofelectric field at the point C

(c)

Two equal charges q arethird charge -2q is placedenergy of the system is

2

[MP PMT 1997]

(b)V2q

(d) ^5-

placed at a distance of 2a and aat the midpoint. The potential

[MP PMT 1997]

IW *«*

(d)

62.

63.

64.

65.

66.

67.

68.

Electrostatics 989

61. Two point charges 100 juC and 5 //C are placed atpoints A and B respectively with AB=40 cm. The workdone by external force in displacing the charge 5 //C

from 6 to C, where BC = 30 cm , angle ABC = — and

= 9x l0 9 Nm 2 /C 2 [MP PMT 1997]

9J

(c) -25

(b)

(d) -4<

The unit of intensity of electric field is [MP PMT/PET 1998](a) Newton/Coulomb (b) Joule/Coulomb

(c) Volt-metre (d) Newton/metre

Equal charges are given to two spheres of different radii.The potential will [MP PMT/PET 1998; MH CET 2000](a) Be more on the smaller sphere

(b) Be more on the bigger sphere

(c) Be equal on both the spheres

(d) Depend on the nature of the materials of the spheres

The electric potential at a point in free space due to a chargeQ coulomb is Q x 10n volts. The electric field at the point is

[CBSE PMT 2008]

(a) 4;re0 Q x l 0 2 0 V / m (b) 12;re0 Qx l0 2 2 V/m

(c) 4;re0 Q x l 0 2 2 V / m (d) 12;re0 Q x l 0 2 0 V / m

A charge of 5C is given a displacement of 0.5m. The workdone in the process is 10J. The potential difference betweenthe two points will be [MP PET 1999](a) 2V (b) 0.25V

(c) IV (d) 25V

The electric potential V is given as a function of distance x

(metre) by V = (5x2 + lOx - 9)volt. Value of electric field at

x = 1 Is [MP PET 1999; Similar KCET 2007]

(a) -20V/m (b) 6 V / m

(c) HV/m (d) -23V/m

Two metal pieces having a potential difference of 800V are0.02m apart horizontally. A particle of mass 1.96x 10~l5fcg issuspended in equilibrium between the plates. If e is theelementary charge, then charge on the particle is

[MP PET 1999]

(a) e . (b) 3e

(c) 6e (d) 8e

The figure shows some of the electric field linescorresponding to an electric field. The figure suggests

[MP PMT 1999]

(a) EA > EB > Ec

(c) EA=EC> EB

E A = E B = E C(d) EA=EC<EB

990 Electrostatics

69. Two spheres of radii a and b respectively are charged andjoined by a wire. The ratio of electric field of the spheres is

[CPMT 1999; JIPMER 2000; RPET 2000; MP PMT 2006]

(a) alb (b) b/a

(c) a2 / fa 2 (d) fa2 /a2

70. A particle of mass m and charge q is placed at rest in a

uniform electric field £ and then released. The kineticenergy attained by the particle after moving a distance y is

[CBSE PMT 1998; Kerala PMT 2005; Kerala PET 2009]

q£y2

71.

(b) q£2y

(d) q2Ey

A hollow insulated conducting sphere is given a positivecharge of 10//C. What Will be the electric field at the centre

of the sphere if its radius s 2 meters

(a) Zero

- (c)

72. An electron of mass m

[CBSE PMT 1998]

(b) 5 fjCm'2

(d) 8//Cm'2

initially at rest moves through a

certain distance in a uniform electric field in time tl. A

proton of mass mp also initially at rest takes time tz to

move through an equal d stance in this uniform electric field.

(c) (m e /mJ1 / 2

Neglecting the effect of gravity, the ratio of t2 111 is nearly

equal to

(a) 1 (b) (m p /m e

(d) 1836

i[JIT 1997 Cancelled]

1/2

73. A cube of side b has a charge q at each of its vertices. Theelectric field due to this charge distribution at the centre ofthis cube will be [KCET 1994, 2000; RPMT 2006]

(a) q/b2

(c) 32q/b2

(b) q/2b2

(d) Zero

74. A charged water drop jwhose radius is 0.1//m is in

equilibrium in an electric j field. If charge on it is equal tocharge of an electron, theh intensity of electric field will be

(g = 10ms !) [RPET 1997; Similar MH CET 2004]

(a) 1.61N/C

(c) 262N/C

75. Four charges are placed orfigure having side of 5cm

electric field intensity at centre will be

(a) 1.02xl07N/C upwards

(b) 2.04xl07JV/C dow wards

(c) 2.04xl07N/C upwards

(d) 1.02xl07/V/C downlvards

(b) 26.2N/C

(d) 1610N/C

corners of a square as shown inIf Q is one microcoulomb, then

Q[RPET 1999]

-2Q

76. A sphere of radius 1cm has potential of 8000 V, thenenergy density near its surface will be [RPET 1999]

(a) 64xl05J/m3 (b) 8xl03J/m3

(c) 32J/m3 (d) 2.83 J /m 3

77. Point charges +4q, -q and +4q are kept on the x-axis atpoints x=0, x=a and x=2a respectively, then

[CBSE PMT 1992](a) Only q is in stable equilibrium(b) None of the charges are in equilibrium(c) All the charges are in unstable equilibrium(d) All the charges are in stable equilibrium

78. Two point charges of 20//C and 80//C are 10cm apart.Where will the electric field strength be zero on the linejoining the charges from 20//C charge

[RPET 1997; Similar VITEEE 2006](a) O.lm (b) 0.04m

(c) 0.033m (d) 0.33m

79. Consider a thin spherical shell of radius R consisting ofuniform surface charge density a. The electric field at apoint of distance x from its centre and outside the shell is

[J & K CET 2008](a) Inversely proportional to a

(b) Directly proportional to x2

(c) Directly proportional to R

(d) Inversely proportional to x2

80. If a charged spherical conductor of radius 10cm has

potential V at a point distant 5 cm from its centre, then the

potential at a point distant 15cm from the centre will be

[SCRA 1998; JIPMER 2001, 02]

1 , ,(a)

(0

(b) f V

(d) 3V

81. Two unlike charges of magnitude q are separated by adistance 2d . The potential at a point midway between themis [JIPMER 1999]

1(a) Zero (b)

(c) q_'d

-0 + 2Q

82. What is the potential energy of the equal positive pointcharges of IjuC each held 1 m apart in air [AMU 1999]

(a) 9xHT3J (b) 9xlO-3eU(c) 2eV/m (d) Zero

83. An oil drop having charge 2e is kept stationary betweentwo parallel horizontal plates 2.0 cm apart when a potentialdifference of 12000 volts is applied between them. If thedensity of oil is 900 kg/m3, the radius of the drop will be

[AMU 1999]

(a) 2.0xlO'6m (b) 1.7xl0^m

(c) 1.4x10-*™ (d) l.lxlO~6m

84. The ratio of momenta of pn electron and an a-particle 92.

86.

87.

88.

91.

which are accelerated frorrof 100 volt is

(a) 1

rest by a potential difference[UPSEAT 1999]

(b)

(d)

85. The work done in bringing a unit positive charge frominfinite distance to a point at distance x from a positivecharge Q is W. Then the potential (/> at that point is

[J & K CET 2008]

WQ

(c)

X

W_

X

(b) W

(d) WQ

When a proton is accelerated through IV, then its kineticenergy will be [CBSE PMT 1999; Similar MP PET/PMT 1998;

JIPMER 1999; UPSEAT 2002;Pb. PET 2003; Kerala PET 2007]

(a) 1840 eV (b) 13.6 eV(c) leV (d) 0.54 eVAn electron enters between two horizontal plates separatedby 2mm and having a potential difference of 1000V. Theforce on electron is [JIPMER 1999]

(a) 8xlO"12N

(c) 8xl09 N

(a)

(c) R f i R f

89. Electric charges of +10//C,

8xlO'14N(b)

(d) 8xl014 NTwo metal spheres of radii Rj and R2 are charged to the

same potential. The ratio of (Charges on the spheres is[KCET 1999]

(b) R,:R2

3- R31: K2(d)

- 5//C, - 3//C and +8//C are

placed at the corners of a square of side V2 m. the potentialat the centre of the square is

[KCET (Ei|gg./Med.) 1999; MP PET 2006]

(a) 1.8V

(c) 1.8xl05V90. In the following diagram the

(b)

(d)

l.SxlO6 V

1.8xl04Vwork done in moving a point

charge from point P to point A, B and C is respectively asWA, WB and Wc , then [J & K CET 2005](a) WA = WB = Wc

(b) WA = WB = Wc = 0

(c) WA > WB > Wc

(d) WA<WB<WC

The electric field due to a charge at a distance of 3 m from it

B

is 500 N/coulomb. The nagnitude of the charge is

1= 9xl09

N-i4;z£0 coulomb*

[MP PMT 2000; SMlar Pb. PMT 2001; RPET 2002]

(a) 2.5 micro-coulomb (b) 2.0 micro-cou/omb

(c) 1.0 micro-cou/omb (d) 0.5 micro-coulcmb

93.

94.

95.

96.

97.

99.

Electrostatics 991i .......I. I.

Two charges of 4//C each are placed at the corners A andB of an equilateral triangle of side length 0.2 m in air. The

I M ~2 "• = 9xlOyelectric potential at C is

[EAMCET (Med.) 2000]

(a) 9xl04V (b) 18xl04V

(c) 36xl04V (d) 36xlO~4VElectric field strength due to a point charge of 5//C at adistance of 80 cm from the charge is [CBSE PMT 2000]

(a) 8xl04N/C (b) 7xl04N/C

(c) 5xl04N/C (d) 4xl04N/CTen electrons are equally spaced and fixed around a circleof radius R. Relative to V = 0 at infinity, the electrostaticpotential V and the electric field E at the centre C are

[AMU 2000]

(a) V * 0 and E * 0 (b) V * 0 and E = 0

(c) V = 0 and E = 0 (d) V = 0 and E * 0

Two positive point charges of 12//C and 8juC are 10cmapart. The work done in bringing them 4 cm closer is

[AMU 2000]

(a) 5.8 J (b) 5.8 eV(c) 13 J (d) 13 eV

Three identical point charges, as shown are placed at thevertices of an isosceles right angled triangle. Which of thenumbered vectors coincides in direction with the electricfield at the mid-point M of the hypotenuse [AMU 2000](a) 1

(b) 2

(c) 3

(d) 4

The displacement of a charge Q in the electric field

£ = eji + e2j + e3k is F = ai + bj . The work done is

[EAMCET (Engg.) 2000]

(a) Q(aei+be2) (b)

(c) Q(ei+e2)Va2+b2

If an electron moves from rest from a point at whichpotential is 50 volt to another point at which potential is 70volt, then its kinetic energy in the final state will be

[J & K CET 2005; Similar RPET 1997]

(a) 3.2 x 10-10J (b) 3.2 x 1Q-18J

(c) I N (d) Idyne

There is a solid sphere of radius '/?' having uniformlydistributed charge. What is the relation between electric field'£' (inside the sphere) and radius of sphere '/?' is

[Pb. PMT 2000]

(a) E=/T2 (b) EocR- 1

R3(d)

992 Electrostatics

100. Two charges +5//C and +10//C are placed 20 cm apart.

The net electric field at the mid-Point between the twocharges is [KCET (Med.) 2000]

(a) 4.5xlO6 N/C directed towards +5//C

(b) 4.5 xlO6 N/C directed towards +10//C

(c) 13.5 x 106 N/C directed towards +5//C

(d) 13.5xlO6 N/C directed towards +10//C

101. Which of the following i$ deflected by electric field

(a) X-rays

(c) Neutrons

[CPMT 2000]

(b) y -rays

(d) a -particles

102. As shown in the figure, charges -i-q and -q are placed at

the vertices B and C <]>f an isosceles triangle. The potentialat the vertex A

l-*\ . • r-'•tKEri J

(b) Zero

/r\ • /—0 ^ c

1

is

2q

2 + b 2

q2 + b 2

(-q)

[MP PE1

**\

/ b b >B w" '

+q

103. Charges 4Q, q and Q and placed along x-axis at positionsx = 0,x = / / 2 and x =i

so that force on charge Q is zero

/ , respectively. Find the value of q

[DPMT 2005]

(a) Q (b) Q/2

(c) - Q / 2 (d) -Q

104. A charged particle of rrtass 5x10" kg is held stationary in

space by placing it in a|n electric field of strengthdirected vertically downwards. The charge on the particle is

[EAMCET 2000; Similar Orissa JEE 2002]

(a) -20xlO~5//C

(c)

(b) -5xlO~5//C

(d) 20xlO~5//C

105. Three charges Q, +q ahd -I-q are placed at the vertices of aright-angled isosceles triangle as shown. The net electrostaticenergy of the configuration is zero if Q is equal to

[I1T-JEE (Screening) 2000; Similar Kerala PET 2008]

-q Q

p

2 + A/2

(d) +q

106. Two electric charges \2fjC and -6//C are placed 20 cmapart in air. There will be a point P on the line joining thesecharges and outside the region between them, at which theelectric potential is zero. The distance of P from -6//Ccharge is [EAMCET 2000]

(a) 0.10m (b) 0.15m

(c) 0.20m (d) 0.25m

107. In the given figure distance of the point from A where theelectric field is zero is [RPMT 2000]

A B

WjiCI* 80 cm

(a) 20cm (b) 10cm

(c) 33cm (d) None of these

108. Figures below show regular hexagons, with charges at thevertices. In which of the following cases the electric field atthe centre is not zero [AMU 2000]

q q,

q it •

(D (2)

(4)

(a) 1 (b) 2

(c) 3 (d) 4

109. An electron is moving towards x-axis. An electric field isalong y-direction then path of electron is [RPET 2000]

(a) Circular (b) Elliptical

(c) Parabola (d) None of these

110. An electron enters in an electric field with its velocity in thedirection of the electric lines of force. Then [MP PMT 2000]

(a) The path of the electron will be a circle

(b) The path of the electron will be a parabola

(c) The velocity of the electron will decrease

(d) The velocity of the electron will increase

111. An electron of mass m and charge e is accelerated fromrest through a potential difference V in vacuum. The finalspeed of the electron will be

[MP PMT 2000; AMU (Engg.) 2000]

(a) Vye /m (b) -JeV/m

(c) (d) 2eWm

112. At a point 20 cm from the centre of a uniformly chargeddielectric sphere of radius J.O cm, the electric field is 100V/m. The electric field at 3 dm from the centre of the spherewill be [BCECE 2005]

(a) 150 V/m (b) 125 V/m

(c) 120 V/m (d) Zero

113. The dimension of (1/2) e0E2(e0 : permittivity of free space;

£ : electric field) is [IIT-JEE (Screening) 2000; KCET 2000]

(c)

MLT

Mr1!'2

(b)

(d)

ML2!'2

ML2!'1

114. In the rectangle, shown below, the two comers have chargesqj=-5//C and q2=+2.0//C., The work done in moving acharge +3.0//Cfrom B to A is (take 1/4 ^b=1010N-m2/C2)

[AMU 2001]

th

5 cm

15cm

(a)

(c)

2.8 J

4.5 J

(b) 3.5 J

(d) 5.5 J

115. A cube of a metal is giveiji a positive charge Q. For theabove system, which of the following statements is true

[MP PET 2001]

(a) Electric potential at the surface of the cube is zero

(b) Electric potential within the cube is zero

(c) Electric field is normal to the surface of the cube

(d) Electric field varies within the cube

116. If q is the charge per Unit area on the surface of a

conductor, then the electric'field intensity at a point on thesurface is [MP PET 2001; UPSEAT 2001]

(a) normal to surface (b)

c) - tangential to surface (d) — —

normal to surface

tangential to surface

117. A hollow conducting sphere! of radius R has a charge (+Q)

on its surface. What is the electric potential within the sphereat a distance r=R/3 from its centre

[MP PMT 2001; UPSEAT 2001; MP PET 2001, 02;

RPMT 2003; Orissa JEE 2005]

Zero

(d) -^-^9.v R

118. A spherical conductor of radius 2m is charged to a potentialof 120 V. It is now placed: inside another hollow sphericalconductor of radius 6m. Calculate the potential to which the

(b) 1 Qr

bigger sphere would be raiS' >d

(a) 20V (b) 60V

(c) 80V (d) 40V

[KCET 2001]

Electrostatics 993

119. A charge (-q) and another charge (+Q) are kept at twopoints A and B respectively. Keeping the charge (+Q) fixedat B, the charge (-q) at A is moved to another point C suchthat ABC forms an equilateral triangle of side /. The network done in moving the charge (-q) is [MP PET 2001]

1 Qq 1 Qq

-Qq/ (d) Zero

120. A particle of mass 'm' and charge 'q' is accelerated through apotential difference of V volt, its energy will be [MP PET 2001]

(a) qV (b) mqV

(c) *.m

(d) qmV

121. Two spheres A and B of radius 'a' and 'b' respectively are atsame electric potential. The ratio of the surface chargedensities of A and B is [MP PMT 2001; Kerala PET 2009]

(a) £ (b) *

(d)

122. 4 point charges each +q is placed on the circumference of acircle of diameter 2d in such a way that they form a square.The potential at the centre is [WB-JEE 2008]

(a) 0 «.$

(d> 734d

123. Electric field intensity at a point in between two parallel sheetswith like charges of same surface charge densities ( d ] is

[MP PMT 2001]

G O

(c) Zero

(b)

(d)

124. In an hydrogen atom, the electron revolves around thenucleus in an orbit of radius 0.53xl010 m. Then theelectrical potential produced by the nucleus at the positionof the electron is [Pb. PMT 2001]

(a) -13.6V (b) -27.2V

(c) 27.2V (d) 13.6V

125. Consider two point charges of equal magnitude andopposite sign separated by a certain distance. The neutralpoint between them [Kerala (Engg.) 2001]

(a) Does not exist

(b) Will be in mid way between them

(c) Lies on the perpendicular bisector of the line joining the two

(d) Will be closer to the negative charge

994 Electrostatics126. Three identical charges each of 2//C are placed at the

vertices of a triangle ABC as shown in the figure[Kerala PMT 2006]

131

If AB + AC = 12 cm! and ABAC = 32 cm2, the potentialenergy of the charge at A is

(a) 1.53 J (b) 5.31J

(c) 3.15 J (d) 1.35J

127. A ball of mass 1 g and charge I O C moves from a pointA. where potential is 600 volt to the point B where potentialis zero. Velocity of the ball at the point B is 20 cm/s. Thevelocity of the ball at the point A will be [KCET 2001]

(b) 228 cm/s(d) 168 m/s

electron in an electric field of

(a) 22.8 cm/s(c) 16.8 mis

128. The acceleration ofmagnitude 50 V/cmJ if e/m value of the electron is

1.76xlOnC/fcg, is

(a) 8.8 xlO14 m/sec2

(c) 5.4 xlO12 m/sec2

[CPMT 2001]

(b) 6.2xlO13 m/sec2

(d) Zero

129. Three charges Q, + q and +q are placed at the vertices of

an equilateral triangle of side / as shown in the figure. If the

net electrostatic energy of the system is zero, then Q is equal

to [MP PET 2001; Kamataka CET 2008; Orissa JEE 2009]Q

(a)

(b)

(c)

(d) Zero +q +q

130. A positively charged particle moving along x-axis with acertain velocity enters a uniform electric field directed alongpositive y-axis. Its [AMU (Engg.) 2001](a) Vertical velocity changes but horizontal velocity remains

constant(b) Horizontal velocitychanges but vertical velocity remains

constant

(c) Both vertical and horizontal velocities change(d) Neither vertical noij horizontal velocity changes

Electric potential at any point is V = -5x + 3y + V15z , then

the magnitude of the electric field is [MP PET 2002]

(a) 3V2 (b) 4V2

(c) 5V2 (d) 7

132. The work done in bringing a 20 coulomb charge from pointA to point B for distance 0.2m is 2J. The potential differencebetween the two points will be (in volt)

[RPET 1999; MP PMT 2002; AIEEE 2002](a) 0.2(c) 0.1

(b) 8(d) 0.4

133. A hollow sphere of charge does not produce an electric fieldat any [MNR 1985; RPET 2001; DPMT 2002;

Kerala PMT 2004; Pb. PET 2004; Orissa PMT 2004](a) Point beyond 2 metres (b) Point beyond 10 metres(c) Interior point (d) Outer point

134. If 4xl020eV energy is required to move a charge of 0.25coulomb between two points. Then what will be thepotential difference between them [MH CET 2002](a) 178V (b) 256V(c) 356V (d) None of these

135. Kinetic energy of an electron accelerated in a potentialdifference of 100 V is [AFMC 1999; MP PMT 2002;

Similar CPMT 1973; MP PET 1989; JIPMER 2002]

(a) 1.6xHT17J (b) 1.6xl021J

(c) 1.6xlO~29J (d) 1.6xlQ-34J

136. A drop of lO^Jcg water carries lO^C charge. What

electric field should be applied to balance its weight (assume

g = 10m/s2) [MP PET 2002](a) 10 V/m upward (b) 10 V/m downward(c) 0.1 V/m downward (d) 0.1 V/m upward

137. A small conducting sphere of radius r is lying concentricallyinside a bigger hollow conducting sphere of radius R. Thebigger and smaller spheres are charged with Q and q(Q>q)and are insulated from each other. The potentialdifference between the spheres will be

[Kamataka CET 2008]

-f--ll <b> zM!+. r R ) 4^-n I R(a)

1R

(d)R

138. Two point charges +9e and +e are at 16 cm away fromeach other. Where should another charge q be placedbetween them so that the system remains in equilibrium

[MP PET 2002]' (a) 24cmfrom+9e (b) 12 cm from+9e

(c) 24 cm from +e (d) 12 cm from +e139. If 3 charges are placed at the vertices of equilateral triangle

of charge 'q' each. What is the net potential energy, if theside of equilateral A is / cm [AIEEE 2002]

1 ~2 1 2q2a) ^r-^

3q2

(b)

(d)

140. The distance between charges 5xlO~nC and -2.7xlO-nCis 0.2 m. The distance at which a third charge should beplaced in order that it will not experience any force alongthe line joining the two charges is [Kerala PET 2002](a) 0.44m ' (b) 0.65m(c) 0.556m (d) 0.350m

141. If identical charges (-q) are placed at each corner of a cubeof side b, then electric potential energy of charge (+q) whichis placed at centre of the cube will be [CBSE PMT 2002]

(a) (b)

(d)

-8V2V

-4g2

142. An electron having change 'e' and mass 'm' is moving in auniform electric field E. Its acceleration will be [AIIMS 2002]

(a)em

eEm

(b)

(d)

m

mE

143. Cathode rays travelling from east to west enter into region ofelectric field directed towards north to south in the plane ofpaper. The deflection of cathode rays is towards [CPMT 2002]

(a) East (b) South

(c) West

144. In the figure, a proton

(d) North

moves a distance d in a uniform

electric field £ as showri in the figure. Does the electric fielddo a positive or negati re work on the proton? Does theelectric potential energy Df the proton increase or decrease

[AIIMS 2007](a) Negative, increase £

(b) Positive, decrease

(c) Negative, decrease

(d) Positive, increase

145. A simple pendulum of period T has a metal bob which isnegatively charged. If it is allowed to oscillate above apositively charged metal plate, its period will

[CBSE PMT 2001; AIEEE 2002](a) Remains equal to T (b) Less than T

(c) Greater than T (d) Infinite

A charged particle of mass m and charge q is released fromrest in a uniform electric field E. Neglecting the effect ofgravity, the kinetic energy of the charged particle after 'f

146.

second is

Eq2m(a)

2t2

E2q2t2

2m

[KCET 2003]

(b)

(d)

2EVmq

Eqmt

147. A proton is about 1840 times heavier than an electron.When it is accelerated bykinetic energy will be

(a) 1840 keV

(c) 1 keV

a potential difference of 1 kV, its[DCE 2001; AIIMS 2003]

(b) 1/1840 keV

(d) 920 keV

148. A conducting sphere of rftdius /?=20 cm is given a charge

Q=l6/uC. What is E at centre [BHU 2003]

(b) 1.8xl06N/C

(d) 0.9xl06N/C

(a) 3.6xl06N/C

(c) Zero

149. A thin spherical conducting shell of radius R has a charge q.Another charge Q is placed at the centre of the shell. Theelectrostatic potential at a| point p a distance R/2 from the

(AIEEE 2003; Similar DCE 2006]centre of the shell is

M (£±0)1R

2q2Q

(b)

(d)

2Q

2Q

Electrostatics 995

150. A hollow conducting sphere is placed in an electric fieldproduced by a point charge placed at P as shown in figure.Let VA, VB, Vc be the potentials at points A, B and Crespectively. Then [Orissa JEE 2003]

VC>VB VB>VC(b)

(c) VA>VB (d) VA=VC

151. A point charge is kept at the centre of a metallic insulatedspherical shell. Then [Orissa JEE 2003](a) Electric field out side the sphere is zero(b) Electric field inside the sphere is zero(c) Net induced charge on the sphere is zero(d) Electric potential inside the sphere is zero

152. An electron moving with the speed 5xl05m per sec is

shooted parallel to the electric field of intensity 1 x 103N/C .

Field is responsible for the retardation of motion of electron.Now evaluate the distance travelled by the electron before

coming to rest for an instant (mass of e = 9xlO'31Kg.

charge =1.6xlO~19C) [MP PMT 2003]

(a) 7m (b) 0.7mm(c) 7cm (d) 0.7cm

153. An electron enters in high potential region V2 from lower

potential region Vj then its velocity [MP PMT 2003]

(a) Will increase(b) Will change in direction but not in magnitude(c) No change in direction of field(d) No change in direction perpendicular to field

154. The electric potential at the surface of an atomic nucleus

(Z = 50) of radius 9.0x 10'13 cm is[CPMT 1990; Pb. PMT 2002; BVP 2003; MP PET 2004;

Similar Pb. PET 2003]

(a) 80 volts (b) 8 x 106 volts

(c) 9 volts (d) 9 x 105 volts

155. The figure shows the path of a positively charged particle 1through a rectangular region of uniform electric field asshown in the figure. What is the direction of electric field andthe direction of particles 2, 3 and 4 [AIIMS 2007]

Top

(b) Top; down, down, top

(d) Down; top, down, down

Down

(a) Top; down, top, down

(c) Down; top, top, down

156. A particle has a mass 400 times than that of the electron andcharge is double than that of a electron. It is accelerated by5V of potential difference. Initially the particle was at rest,then its final kinetic energy will be

[MP PMT 1990; DPMT 1999]'a) 5eV(c) 100 eV

(b) 10 eV• d) 2000 eV

996 Electrostatics157. Two point charges -q and +q are located at points (0,0 -a)

and (0, Oa) , respectively. The potential at a point (0,0,z)where z > a is [EAMCET 2009]

qa

2qa

(b)

(d)2qa

+a

158. An uniform electric field E exists along positive x-axis. Thework done in moving a charge 0.5 C through a distance 2 malong a direction making an angle 60° with x-axis is 10 J.Then the magnitude of electric field is [Kerala PMT 2009]

(a) SVrrT1

(c) VsVrrT1

(e) 20 VrrT1

(b)

(d)

2Vm"

40Vrr

159. Four point +ve charges o same magnitude (Q) are placedat four corners of a rigid square frame as shown in figure.The plane of the frame is perpendicular to Z - axis. If a -vepoint charge is placed at d distance z away from the aboveframe (z«L) then Q! Q [AIIMS 2005]

Z-axis

411Q

(a)(b)(c)

(d)

(a)

(c)

87.5150

(b)(d)

161.

- ve charge oscillates along the Z-axis.It moves away from the frameIt moves slowly towards the frame and stays in theplane of the frameIt passes through the frame only once.

160. A charge of 10 e.s.u. is placed at a distance of 2 cm from acharge of 40 e.s.u. and 4 cm from another charge of 20e.s.u. The potential energy of the charge 10 e.s.u. is (in ergs)

[CPMT 1976; MP PET 1989]112.5250

[AMU (Engg.) 2009]

The electrical potential energy of a system of twoprotons shall increase if the separation between the twois decreasedThe electrical potential energy of a proton electronsystem will increase if the separation between the two isdecreasedThe electrical potential energy of a proton electronsystem will increase if the separation between the two isincreasedThe electrical potential energy of system of twoelectrons shall increase if the separation between thetwo is decreased

A sphere of 4 cm radius is suspended within a hollow sphereof 6 cm radius. The inner sphere is charged to potential 3

Identify the WRONG statement(a)

(b)

(c)

(d)

162.

e.s.u. and the outer sphinner sphere is(a) 54 e.s.u.(c) 30 e.s.u.

ere is earthed. The charge on the[MP PMT 1991]

(b)(d)

1/4 e.s.u.36 e.s.u.

163. Two positive point charges of 12 and 5 microcoulombs, areplaced 10cm apart in air. The work needed to bring them 4cm closer is [AMU (Engg.) 2009](a) 2.4J (b) 3.6J

(c) 4.8 J (d) 6.0 J

164. When a positive q charge is taken from lower potential to ahigher potential point, then its potential energy will

[MP PMT 2006](a) Decrease (b) Increase(c) Remain unchanged (d) Become zero

165. When a negative charge is taken at a height from earth'ssurface, then its potential energy [DPMT 2002](a) Decreases (b) Increases(c) Remains unchanged (d) Will become infinity

166. When a charge of 3 coulomb is placed in a uniform electricfield, it experiences a force of 3000 Newton. Within thisfield, potential difference between two points separated by adistance of 1 cm is [MP PMT 1986, 2000](a) 10 volts (b) 90 note(c) 1000 volts (d) 3000 volts

167. There are two equipotential surfaces as shown in figure. Thedistance between them is r. The charge of -q coulomb istaken from the surface A to B, the resultant work done willbe [MP PMT 1986; CPMT 1986, 88]

(a) W =- l

(b) IV = —!— 4

(0

(d) W = zero168. When one electron is taken towards the other electron, then

the electric potential energy of the system [RPET 1999;CBSE PMT 1993, 99; Pb. PMT 1999; BHU 2000, 02]

(a) Decreases (b) Increases(c) Remains unchanged (d) Becomes zero

169. A hollow metal sphere of radius 5cm is charged such thatthe potential on its surface is 10V. The potential at adistance of 2cm from the centre of the sphere

[MP PET 1992; MP PMT 1996; Similar MP PMT 1990](a) Zero (b) 10 V(c) 4 V (d) 10/3 V

170. The work done in carrying a charge of 5//C from a point Ato a point B in an electric field is lOmJ. The potentialdifference (VB-VA) is then [Haryana CEE 1996](a) +2/cV (b) - 2 f c V(c) + 200 V (d) - 200 V

171. Value of potential at a point due to a point charge is[MP PET 1996]

(a) Inversely proportional to square of the distance(b) Directly proportional to square of the distance(c) Inversely proportional to the distance(d) Directly proportional to the distance

172. Electric potential of earth is taken to be zero because earth isa good [AIIMS 1998; BHU 2002](a) Insulator (b) Conductor(c) Semiconductor (d) Dielectric

173.

174.

175.

176.

There is 10 units of charge at the centre of a circle of radius10m. The work done in mpving 1 unit of charge around thecircle once is

[EAMCET (Med.) 1995; AIIMS 2000; Pb. PMT 2000](a) Zero (b) 10 units(c) 100 units (d) 1 unitTwo parallel plates separated by a distance of 5mm are keptat a potential difference of 50V A particle of mass 10~15/cgand charge 10~nC enters in it with a velocity 107m/s Theacceleration of the particle will be [MP PMT 1997](a) IQPm/s2 (b) 5xl05m/s2

(c) IC^m/s2 (d) 2xl03m/s2

Three point charges ari> placed at the corners of anequilateral triangle. Assurning only electrostatic forces areacting [KCET 2002](a) The system can never be in equilibrium(b) The system will be in equilibrium if the charges rotate

about the centre of the triangle(c) The system will be 'tf\m if the charges have

different magnitudes and different signs(d) The system will be in equilibrium if the charges have the

same magnitudes bu{ different signsIf an insulated non-conducting sphere of radius R hascharge density p. The electric field at a distance r from thecentre of sphere (r < R) will be [BHU 2003]

(c)

(b)

(d)£Q

177. Two plates are at potentials -10 V and +30 V. If theseparation between the plates be 2 cm. The electric fieldbetween them is [Pb. PET 2000](a) 2000 V/m (b) 1000 V/m(c) 500 V/m (d) 3000 V/m

178. The electric potential inside a conducting sphere[RPMT 2002; MP PET 2006;

Similar MP PMT 1986; RPMT 1997](a) Increases from centre to surface(b) Decreases from cenlke to surface(c) Remains constant fri(d) Is zero at every poin

m centre to surfaceinside

179. The wrong statement about electric lines of force is[RPMT 2002]

(a) These originate frpm positive charge and end onnegative charge

(b)(c)(d)

They do not intersect each other at a pointThey have the same form for a point charge and a sphere

180.They have physical :existence

Two infinitely long parallel conducting plates having surfacecharge densities +crand -a respectively, are separated by asmall distance. The medium between the plates is vacuum.If £Q is the dielectric permittivity of vacuum, then the electricfield in the region between the plates is [AIIMS 2005;

Similar AIIMS 2006; MP PMT 2006; UP CPMT 2006]

(a) 0 volts I meter (b)2e.

- volts I meter

(c) — volts I meter2a , ,

(a) volts I meter£„

Electrostatics 997

181. A charged particle is suspended in equilibrium in a uniformvertical electric field of intensity 20000 V/m. If mass of theparticle is 9.6xlO~16 fcg, the charge on it and excess numberof '.ectrons on the particle are respectively (g=10 m/s2)

[Pb. PMT 2003](a) 4.8xlO-19C,3 (b) 5.8xlQ-!9C,4(c) 3.8xlO-19C, 2 (d) 2.8xlO-19C. 1

182. Three infinitely long charge sheets are placed as shown infigure. The electric field at point P is

[IIT-JEE (Screening) 2005]

(b ) -^ fce0

. . 4<r -(c) k

Co

-20.P

-O

(d) -— k£0

183. Four charges +Q, -Q, +Q, -Q are placed at the corners ofa square taken in order. At the centre of the square

[RPMT 2003](a) £ = 0, V = 0 (b) E = 0, V*0(c) E*0, V = 0 (d) E*0, V*0

184. Top of the stratosphere has an electric field E (in units ofV / m ) nearly equal to [DUMET 2009](a) 0 (b) 10(c) 100 (d) 1000

185. Charges q, 2q, 3q and 4q are placed at the corners A, B, Cand D of a square as shown in the following figure. Thedirection of electric field at the centre of the square is along

c [MP PMT 2004]

A B(a) AB (b) CB(c) BD (d) AC

186. Point charges ql = 2//C and q2 = -1//C are kept at points

x = 0 and x = 6 respectively. Electrical potential will bezero at points [MP PMT 2004; Kerala PMT 2010](a) x = 2 and x = 9 (b) x = 1 and x = 5(c) x = 4 and x = 12 (d) x = -2 and x = 2

187. Equipotential surfaces associated with an electric field whichis increasing in magnitude along the x-direction are

[AIIMS 2004](a) Planes parallel to yz-plane(b) Planes parallel to xy-plane(c) Planes parallel to xz-plane(d) Coaxial cylinders of increasing radii around the x-axis

188. A bullet of mass 2 gm is having a charge of 2,wC. Throughwhat potential difference must it be accelerated, startingfrom rest, to acquire a speed of 10 m/s [CBSE PMT 2004](a) 5fcV !b) 50 fcV(c) 5V (d) 50V

998 Electrostatics

189. The points resembling equal potentials are

(a) PandQ

(b) SandQ

(c) Sand/?

(d) PandR

ST

R

[Orissa PMT 2004]

190. Figure shows three points A, B and C in a region of uniform

electric field £. The line AB is perpendicular and BC isparallel to the field lines. Then which of the following holdsgood. Where VA, VB and Vc represent the electric potential atpoints A, B and C respectively

[CPMT 2004; MP PMT 2005; RPMT 2006; BHU 2006]

(a) V,=VB=VC

(b) VA =VB>VC

(c) VA=VB<VC

(d) VA>VB = VC

--•c

191. In a certain charge distribution, all points having zeropotential can be joined by a circle S. Points inside S havepositive potential and points outside S have negativepotential. A positive charge, which is free to move, is placedinside S [DPMT 2004](a) It will remain in equilibrium

(b) It can move inside S, but it cannot cross S

(c) It must cross S at some time

(d) It may move, but will ultimately return to its starting point

192. Infinite charges of magnitude q each are lying at x =1, 2, 4,8... meter on X-axis. The value of intensity of electric field atpoint x = 0 due to these charges will be [J & K CET 2004]

(a) 12xl09qN/C

(c) 6xl09qN/C

(b) Zero

(d) 4xl09qN/C

193. A square of side 'a' has charge Q at its centre and charge 'q'at one of the corners. The work required in moving thecharge 'q' from one corner to the diagonally opposite corner

[UPSEAT 2004]

Zero

(c)

(b)

(d)

Qq

4;re0 a

Qq

194. A pendulum bob of mass 30. 7x10^ kg and carrying a

charge 2xlO~8 C is at rest, in a horizontal uniform electric

field of 20000 V/m. The tension in the thread of the

[UPSEAT 2004]pendulum is (g = 9.8 m / s2]

(a)

(c)

3x10" N (b) 4xlO~4JV

(d)

195. An infinite line charge produce a field of 7.182xl08N/C at adistance of 2 cm. The linear charge density is [MH CET 2004]

(a) 7.27xlO"C/m (b) 7.98x10^ C / m

(c) 7.11xlO-4C/m (d) 7.04x10^ C . - n

196. Two thin wire rings each having a radius R are placed at adistance d apart with their axes coinciding. The charges onthe two rings are +q and -q. The potential differencebetween the centres of the two rings is [AIEEE 2005]

(a) Zero

(c)

(b)

(d)

Q

lR2+d2

197. Positive and negative point charges of equal magnitude are

kept at 0,0,— and 0,0,— , respectively. The work

done by the electric field when another positive point chargeis moved from (-a, 0, 0) to (0, a, 0) is [HT-JEE 2007]

(a) Positive

(b) Negative

(c) Zero

(d) Depends on the path connecting the initial and finalpositions

198. As per this diagram a point charge +q is placed at the originO. Work done in taking another point charge -Q from thepoint A [co-ordinates (0, a)] to another point B [co-ordinates(a, 0)] along the straight path AB is [CBSE PMT 2005]

(a) Zero

(b)

qQ 1

(d) O X

199. Two charges q^ and q2 are placed 30 cm apart, as shown inthe figure. A third charge q3 is moved along the arc of acircle of radius 40 cm from C to D. The change in the

potential energy of the system is k , where k is

[CBSE PMT 2005]

(a) 8q2

(b) 8qj 40cm

(c)

(d)

6q2

A 30 cm B

200. A charged ball B hangs from a silk thread S, which makesan angle 8 with a large charged conducting sheet P, asshown in the figure. The surface charge density a of thesheet is proportional to

(a) sin 0

(b) tantf

(c) cos6>

(d) cot 0

[AIEEE 2005]

201. Two point charges +8q and -2q are located at x = 0

and x = L respectively. The location of a point on the x-axis at which the net electric field due to these two pointcharges is zero is [AIEEE 2005; BCECE 2006]

(a) 8L (b) 4L

(c) 2L

202. Consider E: = xi + j and E^ = xy2i + x2y j; then

[RPMT 2001]

(a) Only El is electrostatic, (b) Only E2 is electrostatic

(c) Both are electrostatic (d) None of these

203. Two insulating plates are b6th uniformly charged in such away that the potential difference between them isV2 - Vj = 20V. (i.e. plate £ is at a higher potential). The

plates are separated by d i= O.lm and can be treated asinfinitely large. An electron is released from rest on the innersurface of plate 1. What is its speed when it hits plate 2

.LlxlO~31/cg) [AIEEE 2006]

O.lm

C, me =9.

(a) 7.02xl012m/s

(b) 1.87xlO°m/s

(c) 32xlO-19m/s

(d) 2.65xl06m/s 1

204. Two spherical conductors A and B of radii 1 mm and 2 mm areseparated by a distance of 5 cm and are uniformly charged. Ifthe spheres are connected by a conducting wire then inequilibrium condition, the ratio of the magnitude of the electricfields at the surfaces of sphetes A and B is [AIEEE 2006]

(a) 1:2

1 :4

(b) 2 : 1

(d) 4:1

205. The potential on the hollow sphere of radius 1 m is 100 volt. Thepotential at 1/4 m from the centre of sphere is [MP PMT 2010]

(a) 1000 volt

(c) 250uo/t

206. The spatial distribution o

(b) 500uo/t

(d) Ooo/t

the electric field due to charges(A,B) is shown in figure. Which one of the followingstatements is correct [AIIMS 2006; Similar HT-JEE 2010]

(a) A is +ueandB-ue and |A|> |B|

(b) A is -ve and B +ve;

(c) Both are +ve but A >

(d) Both are -ve but A >

207. Let V be the electric pelectric field Ex along x direction at that point is given by

[MP PET 2006]

(c) -

Vdx

dVdx

B

tential at a given point. Then the

(b)dx

dx

Electrostatics 999

208. A hollow conducting spherical shell of radius R is chargedwith Q coulomb. The amount of work done for moving anycharge q from the centre to the surface of the shell will be

[DCE 2006]

(b) Zero

Qq Qq(d)

209. What is not true for equipotential surface for uniform electricfield [AFMC 2006]

(a) Equipotential surface is flat

(b) Equipotential surface is spherical

(c) Electric lines are perpendicular to equipotential surface

(d) Work done is zero

210. Figure shows a triangular array of three point charges. Theelectric potential V of these source charges at the midpoint Pof the base of the triangle is [VITEEE 2006]

ql =

0.3m

0.2 m p 0.2 mq 2=-2xlO 6C

= 9xl09Nm2C~2

211.

(a) 55 JcV (b) 45 W

(c) 63 kV (d) 49fcV

Charges +q and -q are placed at points A and Brespectively which are a distance 2L apart, C is the midpointbetween A and B. The work done in moving a charge +Qalong the semicircle CRD is [CBSE PMT 2007]

R

(a)

(c)

A

qQ

C B D

qQ4tfe0 L

qQ6;re0 L

2;re0L

(d) - qQ6;re0 L

212. Charge Q is placed on each of (n-1) corners of a polygon ofn sides. The distance of centre of the polygon from eachcorner is V, then electric field at centre is [MP PET 2007]

(c) n l Q(n-l)4;re0 r2

(d) Zero

1000 Electrostatics

213. A regular hexagon of side 'a' has a charge Q at each vertex.

Potential at the centre f the hexagon is \K =

Zero

(c) 12KQ

214. Charges +2q, + q and

[MP PET 2007]

(b)KQ

Volts

(d) 6a

+q are placed at the corners A, B

and C of an equilateral triangle ABC . If E is the electricfield at the circumcenttre O of the triangle, due to thecharge +q , then the | magnitude and direction of the

resultant electric field at O is [Kerala PET 2007]

(a) £ along AO

(c) £ along BO

215.

(b) 2£ along AO

(d) E along CO

N identical drops of me,rcury are charged simultaneously to10 volt. When combined to form one large drop, thepotential is found to be 40 volt, the value of N is

[Kerala PET 2007; Similar KCET 2007]

(a) 4 (b) 6

(c) 8 (d) 10

216. The electrostatic potential energy between proton and

electron separated by a distance lA is [Kerala PET 2007]

(a) 13.6eV

(c) 14.4eV

(b)

(d)

27.2eV

1.44eV

217. An electric charge 10~3/JC is placed at the origin (0, 0) of

X - Y co-ordinate system. Two points A and B are situated

at (V2,v2) and (2, 0) respectively. The potential difference

between the points A and B will be [AIEEE 2007]

(a) 9 volt (b) Zero

(c) 2 volt

218. Charges are placed on the

(d) 3.5 volt

vertices of a square as shown. LetE be the electric field and V the potential at the centre. If thecharges on A and B are interchanged with those on D and Crespectively, then [AIEEE 2007]

(a) E remains unchanged, V changes—>

(b) Both £ and V change

(c) E and V remains unchanged—»

(d) £ changes, V remains unchanged

219. The potential at a point x (measured in jum) due to somecharges situated on the x-axis is given by V(x)=20 / (x2-^)Volts. The electric field E atx=4//m is given by

[AIEEE 2007; CBSE PMT (Mains) 2011]

(a) 5/3 Volt I //m and in the -ue x direction

(b) 5/3 Volt / fjm and in the +ve x direction

(c) 10/9 Volt / //m and in the -ve x direction

(d) 10/9 Volt I jUm and in the +vex direction

220. A long, hollow conducting cylinder is kept coaxially insideanother long, hollow conducting cylinder of larger radius. Boththe cylinders are initially electrically neutral [IIT-JEE 2007](a) A potential difference appears between the two cylinders

when a charge density is given to the inner cylinder

(b) A potential difference appears between the two cylinderswhen a charge density is given to the outer cylinder

(c) No potential difference appears between the twocylinders when a uniform line charge is kept along theaxis of the cylinders

(d) No potential difference appears between the two cylinderswhen same charge density is given to both the cylinders

221. The figure below shows the electric field lines due to twopositive charges. The magnitudes EA, £B and £c of the

electric fields at points A, B and C respectively are related as[Orissa JEE 2010]

EB>EA> Ec

EA > EK = Er

(a) £^>£ B >£ C (b)

(c) EA = £B > £c (d) i_A ^ L.B = i_c

222. There is a uniform electric field of intensity £ which is asshown. How many labelled points have the same electricpotential as the fully shaded point [Karnataka CET 2010]

(a) 2(b) 3(c) 8(d) 11

O O O0 + 00 0 0Q O Q

223. The electrostatic potential of a uniformly charged thinspherical shell of charge Q and radius R at a distance r fromthe centre is [J & K CET 20 1 0]

for points outside and for points inside

(b)

the shell

Q for both points inside and outside the shell

(c) Zero for point outside and Q for points inside the shell

(d) Zero for both points inside and outside the shell.224. A negatively charged oil drop is prevented from falling under

gravity by applying a vertical electric field 100 V m":. If the

mass of the drop is 1.6x10 g, the number of electrons

carried by the drop is (g = lOms^2) [Kerala PET 2010]

(a) 1018 (b) 1015

(c) 106 (d) 109

(e) 1012

225. Identify the false statement.(a) Inside a charged or neutral conductor electrostatic field

226.

is zero(b) The electrostatic fi^ld at the surface of the charged

conductor must be tangential to the surface at any point(c) There is no net charge at any point inside the conductor(d) Electrostatic potential is constant throughout the volume

of the conductor(e) Electric field at the j surface of a charged conductor is

proportional to the slurface charge densityUnder the action of a givlen coulombic force the accelerationof an electron is 2.5xl022m/s2. Then the magnitude ofthe acceleration of a proton under the action of same forceis nearly [AMU (Engg.) 2010](a) 1.6xlCT19m/s2 (b) 9.1xl03V/s2

[Kerala PMT 2010] 231. Three charges, each +q, are placed at the corners of anisosceles triangle ABC of sides BC and AC, 2a. D and E arethe mid points of BC and CA. The work done in taking acharge Q from D to E is [CBSE PMT (Mains) 2011]

(a) Zero A

3qQ(b)

(c) 1.5xl019m/s2 (d) 1.6xl027m/s2

227.

228.

An electron initially at rest falls a distance of 1.5cm in a

uniform electric field of magnitude 2xl04N/C. The timetaken by the electron to fall this distance is

[AMU (Engg.) 2010](b) 2.1xl(T12s(d) 2.9xlCT9s

Consider an electric field E = E0 x, where E0 is a constant.

The flux through the shaded area (as shown in the figure)due to this field is [IIT-JEE 201 1]

(a) 1.3xl02s(c) 1.6xl(T10s

(a, 0, a) (a, a, a)

(a) 2E0a2

229. Four electric charges +q,

corners of a square ofpotential at point A, midway

(0, 0, 0) (0, a, 0)

(b) V2E0a2

(d) -^L-

+ q,-q and -q are placed at the

ide 2L (see figure). The electricbetween the two charges +q

[CBSE PMT (Pre.) 2011]-rq\

+<?%

^ero

1 2qf

9

I

0(I

/,

t ~~Q

Q

\ 2q4^-0 L

1 2q

230. The electric potential V at any point (x, y, z), all in meters inspace is given by V = 4x volt. The electric field at the point(1, 0. 2) in volt/meter, is(a) 16 along positive X-a ds(b) 8 along negative X-a> is(c) 8 along positive X-ax(d) 16 along negative X-axis

[CBSE PMT (Mains) 2011]

4;re0 a

3qQ

(d)

232. The Value (in vacuum) of energy density at a place in aregion of electric field intensity E, due to it, is given by

[MP PET 2011]

(a)

(c)

£0E2(b) -

(d) -^

233. Two conducting spheres of radii 3 cm and 1 cm areseparated by a distance of 10 cm in free space. If thespheres are charged to same potential of 10 V each, theforce of repulsion between them is [Kerala PET 2011]

(a) (I]xlO-9NV •J1

(c) fIjxlO-9N

(e)

(b) |'|

(d)

234. The electric field created by a point charge falls with distancer from the point charge as [MP PET 2010]

(a) - (b) 4r r2

235. Two large vertical and parallel metal plates having aseparation of 1cm are connected to a DC voltage source ofpotential difference X. A proton is released at rest midwaybetween the two plates. It is found to move at 45° to thevertical JUST after release. Then X is nearly [IIT JEE 2012]

lxlQ-5V(a)

(c)

lx!0~7V

lxlO-9V

(b)

(d) lxlO-10V

Electric Dipole'•

An electric dipole when placed in a uniform electric field Ewill have minimum potential energy, if the positive directionof dipole moment makes the following angle with E

[CPMT 1981; MP PMT 1987]

(a) 7t (b) 7tl2

(c) Zero (d)

8.

1002 ElectrostaticsA given charge is situated at a certain distance from anelectric dipole in the end-on position experiences a force F.If the distance of the charge is doubled, the force acting onthe charge will be

[MNR 1986; BHU 2006; Similar VITEEE 2008](a) 2F(c) F/4The electric potential at a

(b) F / 2(d) F/8

point on the axis of an electricdipole depends on the distance r of the point from thedipole as [CPMT 1982; MP PMT 1996, 2002;UPSEAT 2001;

MP PET 2001, 05; RPMT 2005]1

(a)

(c)

(b) -4

(d) ~4

An electric dipole of moment p is placed in the position ofstable equilibrium in uniform electric field of intensity E. It isrotated through an angle ffhom the initial position. Thepotential energy of electric dipole in the final position is

(a) pEcos#

(c) pE(l-cos<?)

[MP PET 1993, 2011](b) pEsintf

(d) -pEcosff

An electric dipole is kept in non-uniform electric field. Itexperiences [DCE 2001; AHMS 2003; AIEEE 2006](a) A force and a torque

(b) A force but not a torque

(c) A torque but not a force

(d) Neither a force nor a torque

An electric dipole consist ng of two opposite charges of

2xlO~6C each separated by a distance of 3cm is placed

in an electric field of 2xl05 N/C. The maximum torque onthe dipole will be [MP PMT 1987; Similar Kerala PMT 2007]

(a)

(c)

(b) 12xlCT3Nm

(d) 24xlO"3Nm

An electric dipole of moment p is placed normal to the

lines of force of electric intensity E, then the work done indeflecting it through an angle of 180° is

[BVP 2003; Similar CBSE PMT 2006](a) pE (b) +2pE

(c) -2pE (d) Zero

Two equal and opposite charge (+q and - q) are situated atx distance from each other, the value of potential at very farpoint will depend upon [MP PET 2009](a) Only on q (b) Only on x

On qx (d) On-2-

The ratio of electric field and potential (E/V) at midpoint ofelectric dipole, for which separation is / [MP PET 2008]

1

c -

(b) ;

(d) None of these

10. The electric field due to a dipole at a distance r on its axis is

[MP PMT 1993; RPET 2001; MP PET/PMT 2002;BCECE 2003; Pb. PMT 2004; MP PET 2007]

(a) Directly proportional to r3

(b) Inversely proportional to r3

(c) Directly proportional to r2

(d) Inversely proportional to r2

11. An electric dipole has a pair of equal and opposite pointcharges q and -q separated by a distance 2x. The axis of thedipole is defined as [J & K CET 2008]

(a) Direction from positive charge to negative charge

(b) Direction from negative charge to positive charge

(c) Perpendicular to the line joining the two charges drawnat the centre and pointing upward direction

(d) Perpendicular to the line joining the two charges drawnat the centre and pointing downward direction

12. An electric dipole of moment p is placed at the origin alongthe x-axis. The electric field at a point P, whose positionvector makes an angle Mwith the x-axis, will make an angle

with the x-axis, where tana = — tan<? [MP PMT 1994]

(a) a (b) 0

(c) 9 + a (d) 9 + 2a

13. An electric dipole is placed along the x - axis at the originO . A point P is at a distance of 20cm from this origin

such that OP makes an angle — with the x-axis. If the«3

electric field at P makes an angle 9 with the x-axis, thevalue of 6 would be [MP PMT 1997]

n(a) - (b)

(d) ton-'l--

14. Electric charges q,q,-2q are placed at the corners of an

equilateral triangle ABC of side / . The magnitude ofelectric dipole moment of the system is [MP PMT 1994]

(a) q/ (b) 2q/

(c) V3q/ (d) 4q/

15. The torque acting on a dipole of moment P in an electric

field £ is [MP PMT 1994; CPMT 2001; J & K CET 2008; 'Similar DCE 2009]

(a) P - E (b) PxE

(c) Zero (d) ExP

16. The electric field at a point on equatorial line of a dipole anddirection of the dipole moment [MP PET 1995]

(a) Will be parallel

(b) Will be in opposite direction

(c) Will be perpendicular

(d) Are not related

18.

20.

24.

25.

Two opposite and equal charges 4xlO~* coulomb whenplaced 2xlO~2cm away, form a dipole. If this dipole isplaced in an external electrjic field 4xl08 newton'coulomb,the value of maximum torque and the work done in rotatingit through 180° will be [MP PET 1996](a) 64xlO^Nmand64x|o^J

(c) 64xlO^Nm and 32x10^(d) 32xlO^Nmand64xJO-4J

If Ea be the electric field strength of a short dipole at a pointon its axial line and Ee thbt on the equatorial line at thesame distance, then

[MP PET 1999, 2007; RPMT 2002; J & K CET 2004](a) Ee = 2Ea (b) E0 = 2Ee

(c) Ea = Ee

19. An electric dipole is placed

(d) None of the above

n an electric field generated by apoint charge [MP PMT 1999](a) The net electric force oh the dipole must be zero(b) The net electric force on the dipole may be zero(c) The torque on the dipqle due to the field must be zero(d) The torque on the dipole due to the field may be zero

A point Q lies on the perpendicular bisector of an electricaldipole of dipole moment />. If the distance of Q from thedipole is r (much larger than the size of the dipole), thenelectric field at Q is proportional to

[CBSE PMT 1998; JIPMER 2001, 02](a) p l and r 2

(c) p2 and r3

(b) p and r2

(d) p and r3

21. If the magnitude of intensity of electric field at a distance xon axial line and at a distance y on equatorial line on agiven dipole are equal, ther) x : y is [EAMCET 1994]

(a) 1:1 (b) 1:V2

(c) 1:2 (d) #2:1

22. An electric dipole in a uniform electric field experiences(When it is placed at an angle tfwith the field) [RPET 2000](a) Force and torque both (b) Force but no torque(c) Torque but no force (d) No force and no torque

23. The electric intensity due to a dipole of length 10 cm andhaving a charge of 500/rtdistance 20 cm from one of the charges in air, is

[CBSE PMT 2001]

(b) 9.28xlO7 N/C

(d) 20.5xlO7 N/C

(a) 6.25xlO7 N/C

(c) 13.1 x II11 N/CElectric potential at an ecjuatorial point of a small dipolewith dipole moment P (r, distance from the dipole) is

[MP PMT 2001]P

Zero

4;rf0r3

The distance between HT

1.28 A. What will be thedistance of 12 A on the axil

(a) 0.13V(c) 13V

', at a point on the axis at a

2P

(b)

(d)

and C/ ions in HC! molecule ispotential due to this dipole at aof dipole [MP PMT 2002]

(b) 1.3V(d) 130V

26. The potential at a point due to an electric dipole will bemaximum and minimum when the angles between the axisof the dipole and the line joining the point to the dipole arerespectively [MP PMT 2002]

(a) 90° and 180° (b) 0° and 90°

(c) 90° and 0° (d) 0° and 180°27. The value of electric potential at any point due to any

electric dipole is [MP PMT 2004]

(a)

(c) k.p - r

(b) k.pxr

(d) k.

28. An electric dipole has the magnitude of its charge as q and

its dipole moment is p . It is placed in a uniform electric

field E. If its dipole moment is along the direction of thefield, the force on it and its potential energy are respectively

[CBSE PMT 2004](a) 2q-E and minimum (b) q - E and p-E

(c) Zero and minimum (d) q - E and maximum

29. The electric field due to an electric dipole at a distance rfrom its centre in axial position is E . If the dipole is rotatedthrough an angle of 90° about its perpendicular axis, theelectric field at the same point will be [J & K CET 2005]

(a) E

(d) 2E

30. What is the angle between the electric dipole moment andthe electric field strength due to it on the equatorial line

[AFMC 2005]

(a) 0° (b) 90°(c) 180° (d) None of these

31. For a dipole q = 2xlO"6C and d = 0.01m. Calculate the

maximum torque for this dipole if E = 5 x 105 N / C

[RPMT 2003]

(a) lxlO~3Nm"1 (b) 10xlO~3Nm J

(c) 10xlO~3Nm (d) lx!02Nm2

32. A molecule with a dipole moment p is placed in an electric

field of strength E. Initially the dipole is aligned parallel tothe field. If the dipole is to be rotated to be anti-parallel tothe field, the work required to be done by an externalagency is [UPSEAT 2004](a) -2pE (b) -pE

(c) pE (d) 2pE

33. An electric dipole of moment p placed in a uniform electric

field E has minimum potential energy when the angle

between p and E is [UPSEAT 2004]

(a) Zero

(c) a

(b)

(d) f

35.

36.

38.

1004 ElectrostaticsA region surrounding a stationary electric dipoles has

[MP PET 1994; Similar Gujarat CET 2007]

(a) Magnetic field only

(b) Electric field only

(c) Both electric and magnetic fields

(d) No electric and magnetic fields

Two electric dipoles of moment P and 64 P are placed inopposite direction on a line at a distance of 25 cm. Theelectric field will be zero at point between the dipoles whosedistance from the dipole

5 cm

(c.) 10cm

of moment P is

, . 25(b) — cm

[MP PET 2003]

(d)13

cm

When an electric dipole P is placed in a uniform electric

field E then at what angle between P and E the value oftorque will be maximum

(a) 90°

(c) 180°

37. Two charges +3.2x 1C

[MP PET 2002]

(b) 0°

(d) 45°

9C and -3.2xlO-9C kept 2.4 Aapart forms a dipole. If it is kept in uniform electric field ofintensity 4xl05 uolt/m then what will be its electrical energyin equilibrium

(a) +3xlO-23J

(c) -6xlCr23J

[MP PMT 2003]

(b) -3xlO-23J

(d) -2xlO-23J

An electric dipole coincides on Z-axis and its mid point is onorigin of the co-ordinate system. The electric field at an axial

point at a distance z from origin is Ejz) and electric field at

an equatorial point at a distance y from origin is E(y) Here

[Gujarat CET 2007]Ew

EM

(a) 1

(c) 3

(b) 4

(d) 2

39. Three point charges +c, -2q and +q are placed at points(x=0, y=a, z=0), (x=0, y=0, z=0) and (x=a, y=0, z=0)respectively. The magnitude and direction of the electric dipolemoment vector of this charge assembly are

[CBSE PMT 2007; AIIMS 2008]

(a) V2qa along + y direction

(b) V2qa along the line joining points (x=0, y=0, z=0)

and (x=a, y=a, z=0)

(c) qa along the line joining points (x=0, y=0, z=0) and(x=a, y=a, z=0)

(d) V2qa along + x direction

40. An electric dipole of length 1 cm is placed with the axismaking an angle of 30° to an electric field of strength

104 MT1. If it experiences a torque of 10-/2 Nm, the

potential energy of the dipole is [Kerala PET 2008](a) 0.245 J (b) 2.45 J(c) 0.0245 J (d) 245.0 J(e) 24.5 J

41. A sample of HCl gas is placed in an electric field of

3xl04 NC"1. The dipole moment of each HCl molecule is

6xlO~3 0cxm. The maximum torque that can act on a

molecule is [VITEEE 2008]

(a) 2xlO-34C2AT1m (b) 2xlQ-34Nm

(c) 18xlO"26Nm (d) O.SxlO34 (T2 N^rrf1

42.

43.

44.

45.

46.

The direction of electric field intensity (E) at a point on the

equatorial line of an electric dipole of dipole moment (p) is

[Kerala PMT 2008]

(a) Along the equatorial line towards the dipole(b) Along equatorial line away from the dipole(c) Perpendicular to the equatorial line and opposite to (p)

(d) Perpendicular to the equatorial line and parallel to (p)

(e) Along the axial line in the direction of (p)

A water molecule has an electric dipole moment

6.4xlO~30cm when it is in vapour state. The distance inmetre between the centre of positive and negative charge ofthe molecule is [DUMET 2009]

(a) 4xl(T10 (b) 4xlQ-n

(c) 4xHT12 (d) 4xlO~13

The electric dipole moment of an electron and a proton 4.3nm apart is [DUMET 2010]

(a) 6.88xlO~28cm

(c) 3.72xHT14c/m

(b) 2.56xlO"29c2/m

(d) Ilxl0-46c2/m

The electric field and the potential of an electric dipole varywith distance r as [J & K CET 2010]

1 1 n 1(a) - and— (b) -and~r r

(c)1 , 1— and —

j

An electric dipole of moment p is placed in a uniform

electric field E . Then [Kerala PMT 2010]—> —»

(i) The torque on the dipole is px E .—> —>

(ii) The potential energy of the system is p.E .

(in) The resultant force on the dipole is zero.(a) (i), (ii) and (iii) are correct

(b) (i) and (iii) are correct and (ii) is wrong(c) Only (i) is correct(d) (i) and (ii) are correct (iii) is wrong(e) (i), (ii) and (iii) are wrong

48.

49.

1.

2.

Consider the following statements about electric dipole andselect the correct ones

51 : Electric dipole morhent vector p is directed from thenegative charge to Hie positive charge.

52 : The electric field of a dipole at a point with positionvector f depends on | r | as well as the angle

between r and p

S3

S4

1 1The electric dipole potential falls off as — and not as —

theIn a uniform electric field, the electric dipole

experiences no net forces but a torque ? = p x £ .[AMU (Med.) 2010]

(a) S2, S3andS4 (b) S3andS4(c) S2andS3 (d) All fourA dipole of electric dipole moment p is placed in a uniformelectric field of strength E. If 6 is the angle between positivedirections of p and £, then the potential energy of theelectric dipole is largest when 0\s [Kerala PET 2011]

a -

(c)

(e)

jt4n2—n3

(b,f(d) Zero

An electric dipole of morrtent 'p' is placed in an electric fieldof intensity '£'. The dipole acquires a position such that theaxis of the dipole makes an angle d with the direction ofthe field. Assuming that the potential energy of the dipole tobe zero when Q =90°, the torque and the potential energyof the dipole will respectively be [CBSE PMT (Pre.) 2012](a) p£sin 0 , -pEcos0\) pEsin 0 , -2pEcos0

(c) p£sin<9, 2pEcos<? (d) pE cos 0 , -pE cos 0

Electric Flux and Gauss's LawA cylinder of radius R and length L is placed in a uniformelectric field £ parallel to the cylinder axis. The total flux forthe surface of the cylinder1 is given by

[CPMT 1975; RPMT 2002; KCET 2004](a) 2*f?2£ (b) 7fR2IE

(c) (7t?lrtR\IE (d) ZeroA disk of radius a/4 having a uniformly distributed charge 6Cis placed in the x-y plane with its centre at (-a 12, 0,0). A

rod of length a carrying a'uniformly distributed charge 8C isplaced on the x-axis from |x = a/4 to x = 5a/4. Two pointcharges -7C and 3C are placed at (a14, -a/4,0) and

(-3a/4, 3a/4, 0), respectively. Consider a cubical surface

formed by six surfaces x = = + a/2, y = ±a/2, z = ±a /2 . The

electric flux through this cubical surface is [IIT-JEE 2009]

(a)

(c)

-2C

IOC

3. An electric charge q is placed at the centre of a cube of sidea. The electric flux on one of its faces will be

[MP PMT 1994, 95; DCE 1999, 2001; AIIMS 2001;RPET 2003; MP PET 2003; CBSE PMT 2003; UPSEAT 2004]

10.

(a) (b)

q (d) -2-

Total electric flux coming out of a unit positive charge put inair is [MP PET 1995, 2008]

(a) e0 (b) £^

(c) (4pe0)^ (d) 4^

For a given surface the Gauss's law is stated as a E • ds = 0 .

From this we can conclude that [MP PMT 1995](a) E is necessarily zero on the surface(b) E is perpendicular to the surface at every point(c) The total flux through the surface is zero(d) The flux is only going out of the surfaceA cube of side / is placed in a uniform field E, where

E = Ei . The net electric flux through the cube is[Haryana CEE 1996]

(a) Zero (b) PE

(c) 4PE (d) 6PEEight dipoles of charges of magnitude e are placed inside acube. The total electric flux coming out of the cube will be

[MP PMT/PET 1998; Kerala PMT 2006; KCET 2006]

8e

(c)

(b)

(d) Zero

A point charge +q is placed at the centre of a cube of sideL. The electric flux emerging from the cube is

[CBSE PMT 1996; AIEEE 2002; BCECE 2003;MP PET 2006; WB-JEE 2010]

_£_en

(a) (b) Zero

(c)6qL2

(d)

A charge q is placed at the centre of the open end ofcylindrical vessel. The flux of the electric field through thesurface of the vessel is [MNR 1998]

(a) Zero (b) -a-

(d)

It is not convenient to use a spherical Gaussian surface tofind the electric field due to an electric dipole using Gauss'stheorem bemuse [AMU 2000](a) Gauss's law fails in this case(b) This problem does not have spherical symmetry(c) Coulomb's law is more fundamental than Gauss's law(d) Spherical Gaussian surface will alter the dipole moment

12.

13.

14.

15.

16.

According to Gauss' Theorem, electric field of an infinitelylong straight wire is proportional to [RPET 2000; DCE 2000](a) r (b) 1/r2

(c) 1/r3 (d) 1/rElectric charge is uniformly distributed along a long str&lghtwire of radius 1mm. The charge per cm length of the wire isQ coulomb. Another cylindrical surface of radius 50 cm andlength 1m symmetrically encloses the wire as shown in thefigure. The total electric flux passing through the cylindricalsurface is [MP PET 2001; Kerala PET 2011]

17.

(a)

(b)

(c)

(d)

1QOQ

10Q

100Q

1m

The S.I. unit of electric flux is [KCET 2001](a) Weber (b) Newton per coulomb

(c) Volt x metre (d) Joule per coulomb

9i> <?2> <?3 and 94 are point charges located at points asshown in the figure and S is a spherical Gaussian surface ofradius R. Which of the following is true according to theGauss's law <s [AMU 2002]

,+£3).dA =

(b) d(£1 +£2+£3) .dA=-

+ 92 + 93

(c) {(£,( q 1 + q 2 + q 3 + q 4 )

(d) None of the above

Gauss's law should be invalid if [Orissa JEE 2002](a) There were magnetic monopoles

(b) The inverse square law were not exactly true

(c) The velocity of light were not a universal constant

(d) None of these

The inward and outward electric flux for a closed

surface in units of N-m2/C are respectively 8x10

and 4xl03. Then the tptal charge inside the surfaceis [where £0 = permittivfity constant]

[MP PMT 2002; KCET 2003]

(a) 4xl03 C

(-4xl03)

(b) -4xl03 C

(d) -4xl03f0C

18.

19.

20.

21.

22.

23.

A sphere of radius R has a uniform distribution of electriccharge in its volume. At a distance x from its centre, forx < R , the electric field is directly proportional to

[MP PMT 1994; AIIMS 1997; BCECE 2005]

1(b) •

x

(c) x (d) x2

The electric intensity due to an infinite cylinder of radius Rand having charge q per unit length at a distancer(r > R) from its axis is [MP PMT 1993; AFMC 2000]

(a) Directly proportional to r2

(b) Directly proportional to r 3

(c) Inversely proportional to r

(d) Inversely proportional to r2

If the electric flux entering and leaving an enclosed surfacerespectively is ft and <j>2 the electric charge inside the

surface will be [AIEEE 2003]

(a) (ft + ft,)£0 (b) (02 - ft, )f0

(C) (ft,+ft,)/£0 (d) (ft,-ft}/£0

What about Gauss theorem is not incorrect [MP PET 2008]

(a) It can be derived by using Coulomb's Law

(b) It is valid for conservative field obeys inverse squareroot law

(c) Gauss theorem is not applicable in gravitation

(d) (A)&(B)both

Shown below is a distribution of charges. The flux of electricfield due to these charges through the surface S is

[AIIMS 2003;^—^~)X° Kerala PMT 2011]

(a) 3q/£0 (b) 2q/£0

(c) q/£0 (d) Zero

Consider the charge configuration and spherical Gaussiansurface as shown in the figure. When calculating the flux ofthe electric field over the spherical surface the electric fieldwill be due to [IIT-JEE (Screening) 2004]

(a) 92 ,-''' ~~\) Only the positive charges

(c) All the charges \

(d) +qj and -ql

Gauss's law is true only if force due to a charge varies as

[MP PMT 2004]

(a)

(c)

(b)

(d)

24.

25.

27.

28.

An electric dipole is put1 in north-south direction in a spherefilled with water. Which Statement is correct [MP PET 1995]

(a) Electric flux is coming towards sphere

(b) Electric flux is coming out of sphere

(c) Electric flux entering into sphere and leaving the sphereare same

(d) Water does not permit electric flux to enter into sphere

Two infinite plane parallel sheets separated by a distance dhave equal and opposite uniform charge densities a.Electric field at a point between the sheets is [MP PET 1999]

(a) Zero

(b) —

29.

(c)a

(d) Depends upon the location of the point

26. The electric flux for Gaussian surface A that enclose the chargedparticles in free space is (given qt = -14 nC, q2 = 78.85 nC,q3 = - 56 nC) [KCET 2005]

Gaussiansurface A

Gaussiansurface B

(a) l&NrrfCr1

(c) 6.32 x 103 Nm2 CH (d) 6.32 x 103 CN'1 rrr2

A hollow cylinder has ai charge q coulomb within it. If (j> is theelectric flux in units of volt-meter associated with the curvedsurface B, the flux linked with the plane surface A in units ofvolt-meter will be [CBSE PMT 2007; AIIMS 2008]

B

if q .}w 0 w \leo }

«' !

(b) q9

(d) J--

A square surface of side L meteres is in the plane of the

paper. A uniform electric field E (volt/m), also in the planeof the paper, is limited only to the lower half of the squaresurface, (see figure), fhe electric flux is SI units associatedwith the surface is [CBSE PMT 2006, 10]

*

'

(a) Zero

(c) EL2/(2f0)

"'

*

*

(b)

(d)

E

EL2

EL2/ 2

30.

31.

32.

33.

Electrostatics 1007

A point charge causes an electric flux of

-1.0xl03Nm2C"1 to pass through a spherical Gaussiansurface of 10.0 cm radius centred on the charge. If theradius of the Gaussian surface were three times, how muchflux would pass through the surface [Gujarat CET 2007]

(a) 3.0xl03Nm2/C (b) -1.0xl03Nm21C

(c) -3.0xl03Nm2 /C (d) -2.0xl03Nm21C

The adjacent diagram shows a charge +Q held on an

insulating support S and enclosed by a hollow sphericalconductor. O represents the centre of the sphericalconductor and P is a point such that OP = x and SP = r.The electric field at point P will be [AMU PMT 2009]

Charge +Q oninsulating support

r;;_-_ V-V----P

x

SP = rOP=x

(a)

(c) 0 (d) None of the above

An infinitely long thin straight wire has uniform linear charge

density of —cm"1. Then, the magnitude of the electrico

intensity at a point 18 cm

£0=8.8xlO-12C2NrrT2}

away is (Given

[EAMCET 2009]

(a) 0.33x10" NCT (b)

The electric charges are distributed in a small volume. Theflux of the electric field through a spherical surface of radius10 cm surrounding the total charge is 20 Vm. The flux overa concentric sphere of radius 20 cm will be

[J & K CET 2008; DCE 2009](a) 20 Vm (b) 25 Vm

(c) 40 Vm (d) 200 Vm

The total electric flux through a cube when a charge 8q isplaced at one corner of the cube is

[Kerala PMT 2009; J & K CET 2010]

(a) £0q (b) ^-q

(d)

34. Gauss's law is valid for

(a) Any closed surface

(b) Only regular close surfaces(c) Any open surface

(d) Only irregular open surfaces

[DUMET 2009]

37.

38.

39.

40.

41.

42.

Gauss law of gravitation is

(a) <j"g-ds = m

(c) cfg-ds = -4 Grnn

[MP PMT 2009]

(b) d g -ds = Gm

(d) All the above

36. Charge motion within the Gaussian surface gives changingphysical quantity

(a) Electric field

(c) Charge

[MP PMT 2010]

(b) Electric flux

(d) Gaussian surface area

Which of the following is the correct statement of Gauss lawfor electrostatics in a region of charge distribution in freespace

(a)

(c)

cJE.ds = 0

cJE.ds = p

[MP PET 2010]

(b)

(d) cJE.ds = £0p

The angle subtended by a c rcular disk of diameter 2 cm at adistance 1000 cm from your eye is [DUMET 2010]

(a) 0.2° (b) 0.002°

(c) 0.11° (d) 0.22°

Gauss's law of electrostatics would be invalid if

[AMU (Med.) 2010](a) There were magnetic monopoles

(b) The speed of light was not a universal constant

(c) The inverse square law ' was not exactly true

(d) The electrical charge was not quantized

The electrostatic potential inside a charged spherical ball is

given by <j> — or +b whefe r is the distance from the

centre; a, fa are constants. Th en the charge density inside theball is [AIEEE2011]

(a) -24m£0r (b) -6a£0r

(c) -24m£Q (d) -6a£0

A charge Q is enclosed by a Gaussian spherical surface ofradius R. if the radius is doubled, then the outward electricflux will [CBSE PMT (Pre.) 2011]

(a) Be doubled (b) Increase four times

(c) Be reduced to half (d) Remain the same

What is the flux through a cube of side 'a' if a point chargeof q is at one of its corner [CBSE PMT (Pre.) 2012]

q(a) *L (b) 8_B£Q

(d) TT-<

Capacitance1. The potential energy of a charged parallel plate capacitor

is U0 if a slab of dielectric constant k is inserted between the

plates, then the new potentia energy will be [MP PET 2009]

(b) U0k2

(d) U02

A capacitor is charged by using a battery which is thendisconnected. A dielectric slab is then slipped between theplates, which results in [NCERT 1980; MP PET 1995;

BHU 1997; Kerala PMT 2011](a) Reduction of charge on the plates and increase of

potential difference across the plates(b) Increase in the potential difference across the plate,

reduction in stored energy, but no change in the chargeon the plates

(c) Decrease in the potential difference acicss the plates,reduction in the stored energy, but no change in thecharge on the plates

(d) None of the aboveThe energy of a charged capacitor is given by the expression( q = charge on the conductor and C = its capacity)

[MP PMT 1989],2 2

(a) q2C

(c) 2qC

The earth has Volumecapacitance would be

A_

V

(c)

(b) -c

(d) 2F'V

(b)

and Surface Area 'A' then[MP PMT 2009]

V_A

(d) 12* e0-0 V

Two conducting spheres of radii Rl and /?2 having charges

Q] and Q2 respectively are connected to each other. There

is [NCERT 1984; MP PMT 2001 ](a) No change in the energy of the system(b) An increase in the energy of the system(c) Always a decrease in the energy of the system(d) A decrease in the energy of the system unless QiR2 = Q2Ri

A series combination of n1 capacitors each of value Cj, is

charged by a source of potential difference 4V. Whenanother parallel combination of n2 capacitors, each of value

C2, is charged by a source of potential difference V, it has the

same (total) energy stored in it, as the first combination has,The value of C2, in terms of C1, is then [CBSE PMT 2010]

16C, 2C,

nl"2

(c) 16^-<

(b)nln2

( d ) 2 -

In a charged capacitor, the energy resides[CPMT 1974; KCET 2000]

(a) The positive charges(b)(c)(d)

Both the positive and negative chargesThe field between the platesAround the edge of the capacitor plates

The energy stored in a condenser of capacity C which hasbeen raised to a potential V is given by

[CPMT 1974; MP PMT 1993; DCE 2002; RPET 2003;Similar Kerala PMT 2009]

(b)

(c) CV (d)2VC

9. Capacitors are used in electrical circuits where appliances need[MP PMT 2009]

(b) Voltage(d) Resistance

sphere is 2m, then capacitance of[MP PMT 2009]

more

(a) Current(c) Watt

10. If the circumference of asphere in water would be

(a) 2700 pF

(c) 2780 pF

11. Eight drops of mercurycharges combine to form

17.

(b)

(d)

2760 pF

2800 pF

of equal radii possessing equala big drop. Then the capacitance

of bigger drop compared to each individual small drop is[MNR 1987; MP PET 1990; MP PMT 2002, 03;

Pb. PET 2004; J & K CET 2005]

(a) 8 times(c) 2 times

12. If the charge on a capacenergy stored in it increathe capacitor is(a) IOC

(c) 30 C

(a) Dielectric constant(c) Dielectric resistance

14. A parallel plate conden;

1 fc' of the oil is

(a) 0.45(c) 1.10

d and the area of eachdielectric constant fc an

(b) 4 times

(d) 32 timestor is increased by 2 coulomb, these by 21%. The original charge on

[WB-JEE 2009](b) 20 C

(d) 40 C13. The potential gradient at which the dielectric of a condenser

just gets punctured is called(b) Dielectric strength(d) Dielectric number

er has a capacitance 50/jF in air

and HQjUF when immersed in an oil. The dielectric constant

[CPMT 1985; J & K CET 2004]

(b) 0.55(d) 2.20

15. Separation between the plates of a parallel plate capacitor is

between the plates, its capacitance becomes

(a)

(c)

-H£pA

d-tfl-1I k

(a) The type of metal u(b) The thickness of pi,(c) The potential appli(d) The separation bet\e potential to which ?

(a) The amount of charge(b) Geometry and size

(c) Both (a) and (b)(d) None of these

ate is A. When a slab of material ofthickness t(t < d) is introduced

[MP PMT 1989]

(b)

(d)£0A

V

16. The capacity of parallel plate condenser depends on[MP PMT 2000; J1PMER 2002]

sedtes

i d across the platesveen the platesconductor is raised, depends on

[KCET 2005]

of the conductor

19.

20.

21.

22.

23.

24.

25.

Electrostatics 1009

A parallel plate capacitor with air between the plates has acapacitance of 9 pF. The separation between its plates is 'd'.The space between the plates is now filled with twodielectrics. One of the dielectrics has dielectric constantfcj = 3 and thickness d/3 while the other one has dielectricconstant k2 = 6 and thickness 2d/3. Capacitance of thecapacitor is now [AIEEE 2008](a) 45 pF (b) 40.5 pF(c) 20.25 pF (d) 1.8pFThe energy required to charge a parallel plate condenser ofplate separation d and plate area of cross-section A suchthat the uniform electric field between the plates is E, is

[CBSEPMT 2008]

en E2Ad (b) ^ EzAd

»f (d) € 0 E 2 / A d

Eight small drops, each of radius r and having same chargeq are combined to form a big drop. The ratio between thepotentials of the bigger drop and the smaller drop is

[CPMT 1983, 89; MP PMT 1989, 94; RPMT 2000]

(a) 8 : 1 (b) 4 : 1

(c) 2 : 1 (d) 1:81000 small water drops each of radius r and chargeq coalesce together to form one spherical drop. Thepotential of the big drop is larger than that of the smallerdrop by a factor of [NCERT 1984; CPMT 1991, 97;

MP PMT 1996; MP PET 2002;Similar MP PET 1991; MP PMT 1994; RPET 2001]

(a) 1000 (b) 100

(c) 10 (d) 1Two large metal plates are placed parallel to each other. Theinner surfaces of plates are charged by +a and -a(Coulomb/m2). The outer surfaces are neutral. The electricfield is in the region between the plates andoutside the plates. [MP PET 2008], , 2a a a

(c) —,zeroe0

(d) zero,

The capacitance of a spherical condenser is 1//F . If thespacing between the two spheres is 1 mm . then the radius of

the outer sphere is [CPMT 1989](a) 30cm (b) 6m(c) 5cm (d) 3mA 500 f f capacitor is charged at a steady rate of

100 //C / second . The potential difference across the

capacitor will be 10 V after an interval of [MP PET 2008](a) 5 sec (b) 25 sec(c) 20 sec (d) 50 secWhen air in a capacitor is replaced by a medium ofdielectric constant K, the capacity [CPMT 1972, 82, 90;

NCERT 1990; MP PMT 1993; MP PET 1994; KCET 1994](a) Decreases K times (b) Increases K times

(c) Increases K2 times (d) Remains constant

27.

1010 Electrostatics

64 drops each having the capacity C and potential V arecombined to form a big idrop. If the charge on the smalldrop isq , then the charge | on the big drop will be

[CPMT 1971; MP PET 1985; MP PET/PMT 1988;Similar AFMC 2006]

(a) 2q (b) 4q

(c) 16q (d) 64q

The capacity of a parallel plate capacitor increases with the[AFMC 1995; MH CET (Med.) 1999]

'a) Decrease of its area (b) Increase of its distance(c) Increase of its area

28. Two parallel plate of area(d) None of the above

A are separated by two differentdielectrics as shown in fic^re. The net capacitance is

[Orissa JEE 2008]

(b)

3d

4dd/2

d/2

29. The capacity of a spherical conductor in MKS system is

[MP PMT 2002; SimHar RPMT 2005; MP PMT 2006]

""-r(d)

30. Can a metal be used as a medium for dielectric [DPMT 1999]

(a) Yes (b) No

(c) Depends on its shape (d) Depends on dielectric

31. The capacitance C of a capacitor is

[i & K CET 2008; DUMET 2010]

(a) Independent of the charge and potential of thecapacitor

(b) Dependent on the charge and independent of potential

(c) Independent of the geometrical configuration of thecapacitor

(d) Independent of the dielectric medium between the twoconducting surfaces of the capacitor

32. The respective radii of the two spheres of a sphericalcondenser are 12 cm and 9 cm. The dielectric constant ofthe medium between them is 6. The capacity of the

[MP PET 1993]

(b) 240 f f

(d) None of the above

condenser will be

(a) 240 pF

(c) 240 F

33. A capacitor of capacitance

and the battery is then disconnected. If it is connected acrossa 2// F capacitor, the energy

(a) 300 fjj

(c) 225 ft]

(e) 100/J

alue 1 n F is charged to 30 V

lost by the system is

[Kerala PET 2008]

(b) 450 fjj

(d) 150 fjj

34.

35.

36.

37.

38.

39.

40.

The energy stored in the capacitor as shown in the figure (a)

is 4.5xl0^6J. If the battery is replaced by another

capacitor of 900 pF as shown in figure (b), then the totalenergy of system is [VITEEE 2008]

+

+-

" 900pF

+ - 100 v(a)

*

+

!b

-

900pF

: 900pF

(a) 4.5xlQ-6J (b) 2.25xlO"6J

(c) Zero (d) 9-xKr6 J

A capacitor of capacity C has charge Q and stored energy isW. If the charge is increased to 2Q, the stored energy will be

[MP PET 1990](a) 2W (b) W/2(c) 4U/ (d) IV / 4Between the plates of a parallel plate condenser, a plate ofthickness tj and dielectric constant /q is placed. In the rest

of the space, there is another plate of thickness £2 and

dielectric constant /c2

condenser will be

(c)

Ae0

Q fc, fcz

The potential difference across the

[MP PET 1993]

(d)

A I f c j kz

A

A cylindrical capacitor has charge Q and length L. If boththe charge and length of the capacitor are doubled, bykeeping other parameters fixed, the energy stored in thecapacitor [VITEEE 2008](a) Remains same (b) Increases two times(c) Decreases two times (d) Increases four times64 identical spheres of charge q and capacitance C each arecombined to form a large sphere. The charge and capacitance ofthe large sphere is[WB-JEE 2008; Similar AMU (Engg.) 1999](a) 64q,C (b) 16q,4C

(c) 64q,4C (d) 16q,64C

Consider a parallel plate capacitor with plates 20 cm by 20cm and separated by 2 mm. The dielectric constant of thematerial between the plates is 5. The plates are connected toa voltage sources of 500 V. The energy density of the fieldbetween the plates will be close to [AMU PMT 2009](a) 2.65J/m3 (b) 1.95 J/m3

(c) 1.38J/m3 (d) 0.69J/m3

A condenser of capacity C is charged to a potentialdifference of Vl. The plates of the condenser are then

connected to an ideal inductor of inductance L . The currentthrough the inductor when the potential difference across thecondenser reduces to V, is

(a)

[CBSE PMT (Mains) 2010]

(b)

(d)

L

C(V2 •

42.

45.

46.

47.

48.

C,V,U and Q are capacitance, potential difference, energystored and charge of parallel plate capacitor respectively.The quantities that increases when a dielectric slab isintroduced between the plates without disconnecting the

[Kerala PET 2009](b) V a n d U(d) VandQ

plate separation is doubled

battery are(a) VandC(c) U a n d Q(e) U but not QThere is an air filled IpF Parallel plate capacitor. When the

and the space is filled with wax,the capacitance increases 1o 2pF. The dielectric constant ofwax is [Haryana CEE 1996; MNR 1998; KCET 2005;

Similar AMU 1995](a)(c)

26

43. The capacity and the erergy stored in a parallel platecondenser with air between

IV0. If the air is replaced Dy glass (dielectric constant = 5)between the plates, the capacity of the plates and the energystored in it will respectively be

(a) 5C0,5W0

44. Force of attraction betweencapacitor is

(c)

A capacitor of capacity Cpotential V in parallel.reduced to half at once,the same. Then to chargeV again, the energy given by the battery will

Tie

the

drops

(a) CV 2 /4

(c) 3CV2/4N identical sphericalV are combined to formnew drop will be

KCET 2000(a) V

(c) VxNA parallel plate capacitor iapart(a) The capacitance increc(b) The potential difference(c) The total charge i(d) The charge and potentialA 6fjF capacitor is cha

Increase in energy will be[CPMT 1987,

(a) 18xlO~4J(c) 4.5xlO~4J

(b) 4(d) 8

its plates are respectively C0 and

/i \1 0(b) 5C0, —-

w the plates of a parallel plate[AFMC 1998]

(b) -4

(d)

(b)

(d)

is connected with a battery ofdistance between its plates is

ajssuming that the charge remainscapacitance upto the potential

be[MP PET 1989]

CV 2 / 2

CV2

3 charged to the same potentiala big drop. The potential of the

[MP PMT 1990, 2001;; Kerala PET 2002; RPMT 2006]

(b) V / N

(d) VxN2 ' '3charged. If the plates are pulled

[DCE 2009]ses

increases

difference remain the same•ged from 10 volts to 20 uolts .

97; Pb. PET 2002; BCECE 2004]

(b) gxlO^J(d)

49.

50.

51.

52.

53.

54.

55.

Electrostatics 1011

As shown in the figure, a very thin sheet of aluminium isplaced in between the plates of the condenser. Then thecapacity | [AIEEE 2003]

Al strip

(a) Will increase (b) Will decrease

(c) Remains unchanged (d) May increase or decrease

An air capacitor is charged with an amount of charge q anddipped into an oil tank. If the oil is pumped out, the electricfield between the plates of capacitor will [DCE 2009]

(a) Increase (b) Decrease

(c) Remain the same (d) Become zero

The outer sphere of a spherical air capacitor is earthed. Forincreasing its capacitance [MP PET 1991]

(a) Vacuum is created between two spheres

(b) Dielectric material is filled between the two spheres

(c) The space between two spheres is increased

(d) The earthing of the outer sphere is removed

The plates of parallel plate capacitor are charged upto 100V.A 2mm thick plate is inserted between the plates. Then tomaintain the same potential difference, the distance betweenthe plates is increased by 1.6mm. The dielectric constant ofthe plate is [MP PMT 1991]

(a) 5 (b) 1.25

(c) 4 (d) 2.5

Force acting upon a charged particle kept between theplates of a charged condenser is F. If one plate of thecondenser is removed, then the force acting on the sameparticle will become [MP PMT 1991]

(a) 0 (b) F / 2

(c) F (d) 2F

Two metallic charged spheres whose radii are 20cm and10cm respectively, have each 150micro-cou/omb positivecharge. The common potential after they are connected by aconducting wire is [MP PMT 1991]

(a) 9xl06uo/ts (b) 4.5xl06 uo/ts

(c) l.SxlO7 volts (d) 13.5xl06uo/ts

A parallel plate air capacitor has a capacitance C. When it ishalf filled with a dielectric of dielectric constant 5, thepercentage increase in the capacitance will be

[Kamataka GET 2006]

(a) 400%

(b) 66.6%

(c) 33.3%

(d) 200%

57.

59.

60.

61.

1012 ElectrostaticsA frictionless dielectric plate S is kept on a frictionless tableT. A charged parallel plate capacitance C (of which theplates are frictionless) is kept near it. The plate S is inbetween the plates. When the plate S is left between theplates [CPMT 1988]

(a) It will remain stationary on the table(b) It is pulled by the capacitor and will pass on the other end(c) It is pulled between the plates and will remain there(d) All the above statements are falsePick out the false statement from the following

[Kerala PMT 2011](a) The direction of eddy

(b)

having a charge q is

current is given by Fleming's righthand ruleA choke coil is a pure inductor used for controllingcurrent in an a.c circt itThe energy stored in a conductor of capacitance C

,2

2C(d) The magnetic energy stored in a coil of self-inductance

1 yL carrying current is -t-L/

(e) Induction coil is agenerating high voltages

58. A capacitor with air as theof 100 volts. If the spaa

powerful equipment used for

dielectric is charged to a potentialbetween the plates is now filled

with a dielectric of dielectric constant 10, the potentialdifference between the plates will be [MP PET 1992](a) 1000 volts (b) 100 volts(c) 10 volts (d) ZeroThe distance between the circular plates of a parallel platecondenser 40mm in diameter, in order to have samecapacity as a sphere of radius 1 metre is [MP PET 1992](a) 0.01 mm (b) 0.1 mm(c) 1.0 mm (d) 10 mmWhen a slab of dielectric material is introduced between theparallel plates of a capacitor which remains connected to abattery, then charge on p|ates relative to earlier charge

[MP PET 1992](a) Is less(b) Is same(c) Is more(d) May be less or mo« depending on the nature of the

material introducedThe capacitance of a metallic sphere will be I/if, if its radiusis nearly

[MP PMT 1992; UPSEAT 1999; MH CET (Med.) 2001](a) 9km(c) l . l lm

62. Energy stored in capacitocapacitor bear a ratio(a) 1:1(c) 1:1/2

(b)(d)

10m1.11 cm

r and dissipated during charging a[MP PMT 2010]

(b)(d)

1 :22 :1

63. The capacitance of a parallel plate condenser does notdepend on [MP PET 1994](a) Area of the plates(b) Medium between the plates(c) Distance between the plates

(d) Metal of the plates64. Between the plates of a parallel plate condenser there is

1mm thick paper of dielectric constant 4. It is charged at100 volt . The electric field in volt / metre between the

plates of the capacitor is [MP PMT 1994](a) 100 (b) 100000(c) 25000 (d) 4000000

65. The electric field between the two spheres of a chargedspherical condenser [MP PMT 1994](a) Is zero(b) Is constant(c) Increases with distance from the centre(d) Decreases with distance from the centre

66. The distance between the plates of a parallel plate capacitoris d . A metal plate of thickness d / 2 is placed between theplates. The capacitance would then be [MP PMT 1994](a) Unchanged (b) Halved(c) Zero (d) Doubled

67. An uncharged capacitor is connected to a battery. Oncharging the capacitor

[MP PMT 1994; MP PET 1997; KCET 2002)

(a) All the energy supplied is stored in the capacitor(b) Half the energy supplied is stored in the capacitor(c) The energy stored depends upon the capacity of the

capacitor only(d) The energy stored depends upon the time for which the

capacitor is charged68. A capacitor is kept connected to the battery and a dielectric

slab is inserted between the plates. During this process[MP PMT 1994]

(a) No work is done(b) Work is done at the cost of the energy already stored in

the capacitor before the slab is inserted(c) Work is done at the cost of the battery(d) Work is done at the cost of both the capacitor and the

battery69. The capacitance of an air capacitor is 15//F the separation

between the parallel plates is 6mm . A copper plate of 3mmthickness is introduced symmetrically between the plates.The capacitance now becomes [MP PMT 1995](a) 5/JF (b) 7.5/zF

(c) 22.5/uF (d) 3Q/uF

70. An air capacitor is connected to a battery. The effect offilling the space between the plates with a dielectric is toincrease [MP PMT 1995](a) The charge and the potential difference(b) The potential difference and the electric field(c) The electric field and the capacitance(d) The charge and the capacitance

71.

74.

75.

A light bulb, a capacijor and a battery are connectedtogether as shown here, with switch S initially open. Whenthe switch S is closed, which one of the following is true

[MP PMT 1995]

(a) The bulb will light up for an instant when the capacitorstarts charging

(b) The bulb will light up when the capacitor is fully charged(c) The bulb will not ligr^t up at all(d) The bulb will light up and go off at regular intervals

72. The potentials of the two plaies of capacitor are + 10V and -10 V. The charge on 0ne of the platescapacitance of the capacilor is(a)(c)

2F0.5 F

73. The diameter of each pla

is 40 C. The[AFMC 2005]

(b)(d)

4F0.25 F

te of an air capacitor is 4cm . Tomake the capacity of thijs plate capacitor equal to that of20cm diameter sphere, t le distance between the plates willbe [MP PET 1996](a) 4xlO~3m(c) 1cm

with air. The differencecondensers formed wheninner sphere is earthed will be(a) Zero (b)

(c) 4/zz-nfa (d)

"3(b) IxKT-m(d) lxlO~3cm

A spherical condenser ha& inner and outer spheres of radiia and b respectively. Th^ space between the two is filled

between the capacities of twoouter sphere is earthed and when

[MP PET 1996]

b-a

The expression for the cajpacity of the capacitor formed bycompound dielectric placed between the plates of a parallelplate capacitor as shown= A)

(a) ^.

-f-

(b)

(c)

(d)

£0A

d1+dz+d3

AKi AK2 AK

76. The intensity of electric fiel

in figure, will be (area of plate[MP PET 1996]

K-C/2-»l

d at a point between the plates ofa charged capacitor [MP PMT 1996](a) Is directly proportional to the distance between the

plates(b) Is inversely proportional to the distance between the

plates(c) Is inversely proportional to the square of the distance

between the plates(d) Does not depend upon the distance between the plates

77.

Electrostatics 1013

The capacity of a condenser in which a dielectric ofdielectric constant 5 has been used, is C. If the dielectric isreplaced by another with dielectric constant 20. the capacitywill become [MP PMT 1996]

C_

4(a (b) 4C

,c) f (d) 2C

78. An insulator plate is passed between the plates of acapacitor. Then the displacement current [UP CPMT 2006]

(a) First flows from A to B and then from B to A

(b) First flows from B to A then from A to B

(c) Always flows from B to A

(d) Always flows from A to B

79. A parallel plate condenser with a dielectric of dielectric constantK between the plates has a capacity C and is charged to apotential V volts. The dielectric stab is slowly removed frombetween the plates and then reinserted. The net work done bythe system in this process is [AIEEE 2007]

(a) i(K-l)CV2 (b) CV2(K-1)/K

(c) (K-l)CV2 (d) Zero

80. A charge of 10~9C is placed on each of the 64 identicaldrops of radius 2cm. They are then combined to form abigger drop. Find its potential [MP PET 1997]

(a) 7.2xl03V (b) 7.2xl02V

(c) 1.44xl02V (d) 1.44xl03V

81. To increase the charge on the plate of a capacitor means to[Gujarat CET 2007]

(a) Decrease the potential difference between the plates(b) Decrease the capacitance of the capacitor

(c) Increase the capacitance of the capacitor(d) Increase the potential difference between the plates.

82. The plates of a parallel plate capacitor of capacity 50//C

are charged to a potential of 100 volts and then separated

from each other so that the distance between them isdoubled. How much is the energy spent in doing so

[MP PET 1997; JIPMER 2000]

(a) 25xlO~2J (b) -12.5xHT2J

(c) -25xlO-2J (d) 12.5xlO-2c7

83. Two spherical conductors each of capacity C are chargedto potentials V and -V . These are then connected bymeans of a fine wire. The loss of energy will be

[MP PMT 1997]

(a) Zero

a/2 (d) 2CV2

85.

86.

87.

88.

89.

90.

91.

1014 ElectrostaticsThe area of the plates of a parallel plate condenser is Aand the distance between the plates is 10mm. There aretwo dielectric sheets in it, one of dielectric constant 10 andthickness 6mm and the other of dielectric constant 5 andthickness 4mm . The capacity of the condenser is

[MP PMT 1997]12

Sn35 c

5000£0A

(b) =:>

(d) 1500 £QA

An air capacitor of capacity C = WjuF is connected to a

constant voltage battery of 12 V. Now the space between

the plates is filled with a liquid of dielectric constant 5. Thecharge that flows now from battery to the capacitor is

[MP PMT 1997](a)

(c)

120//C

480//C(b)(d)

699//C

24//CA parallel plate capacitor is first charged and then adielectric slab is introduced between the plates. The quantitythat remains unchanged is [MP PMT/PET 1998]

Charge Q

Capacity C(b)

(d)

Potential V

Energy UA 2fJF capacitor is charged to lOOuo/f and then its platesare connected by a conducting wire. The heat produced is

[MP PET 1999; Pb. PET 2003; Similar KCET 1992;JIPMER 2000; Orissa JEE 2003; UPSEAT 2004]

(a) 1J (b) 0.1J

(c) 0.01J (d) 0.001J

The force between the plates of a parallel plate capacitor ofcapacitance C and distance of separation of the plates dwith a potential difference

CVZ

(c)

2d

cV2

V between the plates, is[MP PMT 1999]

2 2(b)

(d)

C2V2d2

Two metal spheres of capacitance Cj and C2 carry some

charges. They are put in contact and then separated. Thefinal charges Ql and Q2 on them will satisfy

[MP PMT 1999]

Q2

P,

QL =CL

Q2 C2(b) ^- = -2-

(d) ^<^

A parallel plate condenser with oil between the plates(dielectric constant of oil K = 2 ) has a capacitance C . If theoil is removed, then capacitance of the capacitor becomes

[CBSE PMT 1999; MH CET 2000]

V2C (b) 2C

What is the area of the plates of a 3F parallel platecapacitor, if the separation between the plates is 5mm

[AIIMS 1998; Pb. PET 2000; BHU 2002]

(a) 1.694xl09m2 (b) 4.529xl09m2

(c) 9.281 x!09m2 (d) 12.981 x 109 m2

92.

93.

94.

95.

96.

97.

98.

99.

A parallel plate capacitor has circular plates of 0.08m

radius and 1.0xlO~3m separation. If a P.O. of 100 volt is

applied, the charge will be [ISM Dhanbad 1994]

(a) 1.8xlO-10C (b) 1.8xlO~8C

(c) 1.8xlO~20C (d) None of theseThe capacity of a parallel plate condenser is 10//F without

dielectric. Dielectric of constant 2 is used to fill half thedistance between the plates, the new capacitance in f is

[EAMCET (Engg.) 1995](a) 10 (b) 20

(c) 15 (d) 13.33The energy stored in the condenser is

[EAMCET (Engg.) 1995; CPMT 2000; CBSE PMT 2001]

(a) QV (b) -QV

(c) -<2 C

(a)(b)(c)(d)

A battery is used to charge a parallel plate capacitor till thepotential difference between the plates becomes equal to theelectromotive force of the battery. The ratio of the energystored in the capacitor and the work done by the battery willbe [AIEEE 2007](a) 1 (b) 2(c) 1/4 (d) 1/2Two identical charged spherical drops each of capacitance Cmerge to form a single drop. The resultant capacitance is

[AFMC 1993]Equal to 2CGreater than 2CLess than 2C but greater than CLess than C

The capacitance of a parallel plate capacitor with air asmedium is 3{f. With the introduction of a dielectric mediumbetween the plates, the capacitance becomes 15//F. Thepermitivity of the medium is [Kerala PMT 2007](a) 5 (b) 15(c) O^xlO-^C^-'m-2 (d) 8.854x10-" C2^1™-2

The radius of a metallic sphere if its capacitance is 1/9F, is[KCET 1999; Pb. PET 2001]

(a) 106m (b) 107m(c) 109m (d) 108mThe ratio of charge to potential of a body is known as

[CPMT 1999; MH CET 2001; Pb. PMT 2004](a) Capacitance (b) Conductance(c) Inductance (d) Resistance

100. If the capacity of a spherical conductor is 1 picofarad, thenits diameter, would be [Pb. PMT 1999](a) 1.8xl03m (b) 18xlQ-3m(c) l.SxlO-5™ (d) 18xlO-7m

101. A parallel plate air capacitor is charged to a potentialdifference of V. After disconnecting the battery, distancebetween the plates of the capacitor is increased using aninsulating handle. As a result, the potential differencebetween the plates [KCET 1999; CBSE PMT 2006](a) Decreases (b) Increases(c) Becomes zero (d) Does not change

102. A lOpF capacitor is connected to a 50 V battery. How muchelectrostatic energy is stored in the capacitor

[KCEl| 1999; AFMC 2000; MH CET 2000](a) 1.25X10-8./(c) S.SxlO^J

103. Two protons A and B aia parallel plate capacitForces on protons are F,

(b)

(b) 2.5xlO-7J(d) 4.5xlCT2J

e placed in space between plates ofcharged upto V volts (See fig.)

and FR, then [RPET 1999]

.AB

FA>FB

FA<FB

(c) FA=FB

(d) Nothing can be saic

104. If a slab of insulating material 4xl(T3m thick is introducedbetween the plates ofj a parallel plate capacitor, theseparation between plates has to be increased by

3.5xl(T3m to restore the capacity to original value. The

dielectric constant of the hiaterial will be [AMU (Med.) 1999](b) 8(d) 12

105. When a dielectric material is introduced between the platesof a charged condenser then electric field between the plates

[Pb. PMT 1999, 2004](b) Increases(d) First (b) then (a)

106. A parallel plate capacitor has a plate separation of 0.01 mmand use a dielectric (whose dielectric strength is 19 KV/mm)as an insulator. The max mum potential difference that canbe applied to the terminals of the capacitor is

[AMU (Engg.) 1999]

(a)(c)

610

(a) Decreases(c) Remain constant

(a)(c)

190V95V

(b) 290V(d) 350V

107. A 40 jif capacitor in a defibrillator is charged to 3000 V.The energy stored in the capacitor is sent through thepatient during a pulse of c uration 2ms. The power deliveredto the patient is(a) 45/clV(c) 180 kW

108. Two metallic spheres of

[AHMS 2004](b) 90 kW(d) 360 kW

109.

radii 1cm and 2cm are given

charges 10~2 C and 5xlO~ 2 C respectively. If they are

connected by a conducting wire, the final charge on thesmaller sphere is [CBSE PMT 1995]

(a) 3xlO"2C (b) lxlO~2C

(c) 4xlO'2C (d) 2xlO~2CA variable condenser is permanently connected to a 100 Vbattery. If the capacity is changed from 2//F to 10//F,

then change in energy is edjual to [BHU 2000]

(a) 2xlO~2J (b) 2.5xlO~2J

(c) 3.5xKT2J (d) 4xlO"2J

110. A parallel plate capacitor having a plate separation of 2 mmis charged by connecting it to a 300 V supply. The energydensity is [BHU 2004](a) 0.01J/m3

(c) 1.0 J/m3

(b) 0.1J/m3

(d) 10 J/m3

111. The capacity of a parallel plate condenser is 15//F , when

the distance between its plates is 6 cm. If the distancebetween the plates is reduced to 2 cm, then the capacity ofthis parallel plate condenser will be

[AFMC 2000; CBSE PMT 2001](a) 15/jF (b) 30//F

(c) 45//F (d) 60//F

112. When we touch the terminals of a high voltage capacitor,even after a high voltage has been cut off, then the capacitorhas a tendency to [AFMC 2000](a) Restore energy (b) Discharge energy(c) Affect dangerously (d) Both (b) and (c)

113. In a capacitor of capacitance 20//F , the distance between

the plates is 2mm. If a dielectric slab of width 1mm anddielectric constant 2 is inserted between the plates, then thenew capacitance is [BHU 2000](a) 2/jF (b) 15.5//F

(c) 26.6//F (d) 32//F

114. What is the value of capacitance if the thin metallic plate isintroduced between two parallel plates of area A andseparated at distance d [MP PMT 2010]

(a)

(c)

e0 A(b)

(d)d 2d

115. The capacity of a parallel plate capacitor w'th no dielectricsubstance but with a separation of 0.4 cm is 2ff. Theseparation is reduced to half and it is filled with a dielectricsubstance of value 2.8. The final capacity of the capacitor is

[CBSE PMT 2000](a) ll.2ff (b) 15.6//F(c) 19.2//F (d) 22.4/F

116. Two insulated metallic spheres of 3[f and 5/zF capacitancesare charged to 300V and 500V respectively. The energyloss, when they are connected by a wire is

[CPMT 1999; Pb. PMT 1999, 2001; KCET 2000](a) 0.012 J (b) 0.0213 J

(c) 0.0375 J (d) 3.75 J117. Two conducting spheres of radii 5 cm and 10 cm are given

a charge of 15//C each. After the two spheres are joined bya conducting wire, the charge on the smaller sphere is

[AMU (Engg.) 2001](a) 5fjC (b) 10//C(c) 15//C (d) 20juC

118. In a parallel plate capacitor of capacitance C, a metal sheetis inserted between the plates, parallel to them. If thethickness of the sheet is half of the separation between theplates. The capacitance will be [KCET 2001](a) C/2 (b) 3C/4(c) 4C (d) 2C

119. While a capacitor remains connected to a battery anddielectric slab is applied between the plates, then

[KCET 2001](a) Potential difference between the plates is changed(b) Charge flows from the battery to the capacitor(c) Electric field between the plates increases(d) Energy store in the capacitor decreases

(a) 7.8 mJ

(c) 3.2 mJ

1016 Electrostatics120. A body of capacity 4//F is charged to 80V and another

body of capacity 6 // F is charged to 30V. When they are

connected the energy lost by 4 ju F capacitor is

[EAMCET 2001]

(b) 4.6 mJ

(d) 2.5 mJ

121. The capacity of the conductor does not depend upon[BHU 2001]

(a) Charge (b) Voltage

(c) Nature of the material (d) All of these

A solid conducting sphere of radius Rl is surrounded byanother concentric hollow conducting sphere of radius R2.The capacitance of this assembly is proportional to

[MP PET 2001; UPSEAT 2001]

R2+Rl

12

(a)

! +R2

(b)

(d)

R1R2

R2 -

123. Two spherical conductors A and B of radius a and b (b > a)are placed in air concentrically B is given charge + Qcoulomb and A is grounded. The equivalent capacitance ofthese is

(c)

abb-a

(b)

(d)

[MP PMT 2001]

(a + b)

b-a

124. The energy stored in a condenser is in the form of[J & K CET 2004]

(a) Kinetic energy

(b) Electrostatic potential energy

(c) Elastic energy

(d) Magnetic energy

125. A capacitor is used to store 24 watt hour of energy at 1200volt. What should be the

(a) 120 mF

(c) 24 ff

capacitance of the capacitor[Kerala (Engg.) 2001]

(b) 120 ff

(d) 24 mF

126. The mean electric energy density between the plates of acharged capacitor is (here q= charge on the capacitor andA- area of the capacitor!plate) [MP PET 2002]

(a) r^r (b) -Ar

(d) None of the above

127. A charge of 40//C is givep to a capacitor having capacitanceC=10//F. The stored energy in ergs is [CPMT 2002]

80x10^

80

(b) 800

(d) 8000

. , . ,128. Work done by an external agent in separating the parallel

plate capacitor is [AIEEE 2002]

CV

(0 icV2

(b) -|c2V

(d) None of these

129. A parallel plate capacitor has an electric field of 105 V / m

between the plates. If the charge on the capacitor plate isIfj C , the force on each capacitor plate is[Orissa JEE 2002]

(a) 0.5 N (b) 0.05 N

(c) 0.005 N (d) None of these

130. A parallel plate capacitor has plate area A and separation d.It is charged to a potential difference V0. The chargingbattery is disconnected and the plates are pulled apart tothree times the initial separation. The work required toseparate the plates is [Kerala PET 2002]

(c)

(b)2d

3d

131. The electric field between the plates of a parallel platecapacitor when connected to a certain battery is EQ . If the

space between the plates of the capacitor is filled byintroducing a material of dielectric constant K withoutdisturbing the battery connections, the field between theplates shall be [AMU (Med.) 2002]

(a) K£0 (b)

(d) None of the above

132. If the distance between parallel plates of a capacitor ishalved and dielectric constant is doubled then thecapacitance [BHU 2001; CBSE PMT 2002; MH CET 2003]

(a) Decreases two times (b) Increases two times

(c) Increases four times (d) Remains the same

133. Putting a dielectric substance between two plates ofcondenser, capacity, potential and potential energyrespectively [AFMC 2002]

(a) Increase, decrease, decrease

(b) Decrease, increase, increase

(c) Increase, increase, increase

(d) Decrease, decrease, decrease

134. A thin metal plate P is inserted half way between the platesof a parallel plate capacitor of capacitance C in such a waythat it is parallel to the two plates. The capacitance nowbecomes [Orissa JEE 2002]

(a) C (b) C/2

(c) 4C (d) None of these

135. If there are n capacitors in parallel connected to V volt

source, then the energy stored is equal to [AIEEE 2002]

cv

(c) CV2

136. If n drops, each of capa

big drop, then the ratio

(b)

citance C, coalesce to form a single

of the energy stored in the big drop

to that in each small drop will be

[UPSEAT 2002; Kerala PET 2010]

(a ) n : l

(c) ns/3 : 1

(b) n1/3:l

(d) n 2 : !

137. A conducting sphere of radius 10cm is charged 10//C.

Another uncharged sphere of radius 20 cm is allowed to

touch it for some time. After that if the sphere are separated,

then surface density of charges, on the spheres will be in the

[AIIMS 2002]ratio of

(a) 1:4

(c) 2 :1

(b) 1:3

(d) 1:1

138. 64 small drops of mercury, each of radius r and charge q

coalesce to form a big drop. The ratio of the surface density

of charge of each small drop with that of the big drop is

1 :64

4 :1

[KCET 2002]

(b) 64 : 1

(d) 1:4

139. Capacitance (in F) of a spherical conductor with radius 1m

[AIEEE 2002]

(a) l.lxlO-10

(c) 9xlQ-9

(b)

(d) 10-3

140. On increasing the plate separation of a charged condenser,

the energy [Kerala PMT 2004]

(a) Increases (b) Decreases

(c) Remains unchanged (d) Becomes zero

141. The energy required to charge a capacitor of 5//F by

connecting a d.c. source of20fcVis [Pb. PMT 2002]

(a) lOfcJ (b) 5kJ

(c) 2kJ (d) 1 kJ

142. The capacitance of a parallel plate capacitor is 12/zF. If the

distance between the plates is doubled and area is halved,

then new capacitance will be

[MH CET 2002; Similar RPMT 2005]

(a) 8/zF (b) 6/f

(c) 4//F (d) 3ff

Electrostatics 1017

143. A capacitor of capacitance 6/zF is charged upto 100 volt.

The energy stored in the capacitor is

[BHU 2003; CPMT 2004; MP PMT 2005; RPMT 2006;

Similar AIIMS 1980, 84; AFMC 1988; MP PET 1994;

MP PMT 2000; MH CET 2002]

(a) 0.6 Joule (b) 0.06Jou/e

(c) 0.03 Joule (d) 0.3 Joule

144. A parallel plate air capacitor is charged and then isolated.

When a dielectric material is inserted between the plates of

the capacitor, then which of the following does not change

[Orissa JEE 2003; MP PET 2006]

(a) Electric field between the plates

(b) Potential difference across the plates

(c) Charge on the plates

(d) Energy stored in the capacitor

145. Capacitance of a parallel plate capacitor becomes 4/3 times

its original value if a dielectric slab of thickness t = d/2 isinserted between the plates (d is the separation between the

plates). The dielectric constant of the slab is [KCET 2003]

(a) 8 (b) 4

(c) 6 (d) 2

146. An air filled parallel plate capacitor has capacity C. If

distance between plates is doubled and it is immersed in a

liquid then capacity becomes twice. Dielectric constant ofthe liquid is [BCECE 2004]

(a) 1 (b) 2

(c) 3 (d) 4

147. A spherical drop of capacitance 1 f f is broken into eight

drops of equal radius. Then, the capacitance of each small

drop is [KCET 2004]

(a) !>

(c) -//F

(b) 8//F

(d)

148. The work done in placing a charge of 8 x 10 18 coulomb ona condenser of capacity 100 micro-farad is [AIEEE 2003]

(a) 32xlO~32Joufe (b) 16xlO~32 Joule

(c) 3.1xlO~26Jou/e (d) 4xlO-10Joute

149. 64 drops of mercury each charged to a potential of 10V.They are combined to form one bigger drop. The potential

of this drop will be (Assume all the drops to be spherical)

[MP PET 2003; Similar MP PET 1997]

(a) 160V (b) 80V

(c) 10 V (d) 640V

1018 Electrostatics150. A spherical drop of mercury having a potential of 2.5 V is

obtained as a result of merging 125 droplets. The potentialof constituent droplets wou d be [Orissa JEE 2003]

(b)(a)(c)

1.0 V0.2V (d)

0.5V0.1V

of capacity C0 is charged to a151. A parallel plate capacitorpotential V0

(i) The energy stored in the capacitor when the battery isdisconnected and the separation is doubled El

(ii) The energy stored in the capacitor when the chargingbattery is kept connected and the separation betweenthe capacitor plates is doubled is E2. Then El IE2 valueis [EAMCET 2003]

(a) 4 (b) 3/2(c) 2 (d) 1/2

152. A parallel plate capacitor carries a charge q. The distancebetween the plates is doubled by application of a force. Thework done by the force is [MP PET 2003]

(a) Zero (b) ^-c*

«£153. As in figure shown, if a capacitor C is charged by connecting

it with resistance R, then energy is given by the battery willbe

(b)

(c)

lev2

More than-CV2

Less than -CV2

[MP PMT 2003]

H'R

-^VW '

(d) Zero

154. A capacitor is charged to 200 volt it has 0.1 coulomb

charge. When it is discharged, energy will be [MP PET 2003]

(a) 1J (b) 4J(c) 10 J (d) 20 J

155. When a lamp is connected in series with capacitor, then[Pb. PMT 2004]

(a) Lamp will not glow (b) Lamp will burst out(c) Lamp will glow normally (d) None of these

156. If a dielectric substance is introduced between the plates of acharged air-gap capacitor. The energy of the capacitor will

[MP PMT 2004]

(a) Increase(b) Decrease(c) Remain unchanged(d) First decrease and then increase

157. Which is known as capacitive time constant [MP PMT 2010]

(b) RIC(a) RIL

(c) R/LC (d)

158. The net charge on capacitor is [MP PMT 2010](a) 2q (b) q/2(c) 0 (d) ~

159. A capacitor of capacitance C is charged to a potential V. Theflux of the electric field through a closed surface enclosingthe capacitor is [MP PET 2010]

(c)

CV

CV

(b)2CV

(d) Zero

160. n identical droplets are charged to V volt each. If theycoalesce to form a single drop, then its potential will be

[WB-JEE 2010]

(a) n2/3V (b) n1/3V

(c) nV (d) V/n

161. If the charge on a capacitor is doubled, the value of itscapacitance C will be [DUMET 2010](a) Doubled (b) Halved(c) Remain the same (d) None of these

162. A parallel plate capacitor of a capacitance of 1 farad wouldhave the plate area of about [DUMET 2010]

(a) 100m2 (b) I/cm2

(c) 100/cm2 (d) 1000/cm2

163. A capacitor is charged by a battery and the energy stored isU. The battery is now removed and the separation distancebetween the plates is doubled. The energy stored now is

[J & K GET 2010]

U

2

2U (d) 4Lf

2//F capacitor is charged as shown in figure. Thepercentage of its stored energy dissipated after the switch Sis turned to position 2 is [IIT-JEE 2011]

1 2S

a —

(c164. A

2ffT 8ffT

(a) 0% (b) 20%

(c) 75% (d) 80%

165. A parallel plate condenser has a uniform electric fieldE(V/m) in the space between the plates. If the distance

between the plates is d(m) and area of each plate is A(m2)the energy (joules) stored in the condenser is

[CBSE PMT (Pre.) 2011]

(a) ±e0E2Ad

(0

(b) E2Ad/e0

(d) £0EAd

166. In the given circuit, a charge of +80//C is given to the

upper plate of the 4fjF capacitor. Then in the steady state,the charge on the upper plate ;of the 3//F capacitor is

+80//C ? [IIT-JEE 2012]

2ff~ -3,

+32//C =

448 //C

if

(b) +40 fjC

(d) +80 fjC

Grouping of Capacitors

Two identical capacitors are joined in parallel, charged to apotential V and then separated and then connected in seriesi.e. the positive plate of one is connected to negative of theother [NCERT 1982; KCET 1993](a) The charges on the free plates connected together are

destroyed(b) The charges on the free plates are enhanced(c) The energy stored in the system increases(d) The potential difference ih the free plates becomes 2VThe condensers of capacity Cl and C2 are connected inparallel, then the equivalent capacitance is

[NCERT 1977; KCET 2000; DPMT 2002; MP PMT 2004]

Cj + C2

Q

(b)Q+C2

Co

A parallel plate capacitor is made by stacking n equallyspaced plates connected alternately. If the capacitancebetween any two plates is C then the resultant capacitance is

[DPMT 2001; MP PMT 2003; AIEEE 2005; AIIMS 2007](a) C (b) nC(c) (n-l)C (d) (n + l)CSeven capacitors each of papacity 2//F are to be so

connected to have a equivalent capacity — /jF . Which will

be the necessary figure as shown [IIT-JEE 1990]

(b)

8.

(c)

(d)

HHHH

HHHHH

Four plates of equal area A are separated by equaldistances d and are arranged as shown in the figure. Theequivalent capacity is

2e0A(b)

3e0A

(c) ^P (d) ^d d

Three capacitors each of capacitance C and of breakdownvoltage V are joined in series. The capacitance andbreakdown voltage of the combination will be

[CBSEPMT 2009]

£3' 3

a — ,— (b) 3C,^-

f,3V (d) 3C,3V

A parallel plate capacitor with air as medium between theplates has a capacitance of 10/zF . The area of capacitor is

divided into two equal halves and filled with two media asshown in the figure having dielectric constant fc1=2 andfc2=4. The capacitance of the system will now be

[MP PMT 1987; RPET 2001; Similar AFMC 2006;

VITEEE 2006]

(a) lOff

(b) 20ff

(c) 30/zF

(d) 40//F

Three capacitors are connected to D.C. source of 100 volts

shown in the adjoining figure. If the charge accumulated onplates of C!,C2and C3 are qa, qb,qc,qd.qeandqf

respectively, then

100-(a) qb+qd+q,=—C

(b) qb + qd+q{=0

(c) q a + q c + q e = 5 0 C

(d) qb = qd = qf

[CPMT 1986]

3ff

a fa c d e f

100 Vote

10.

11.

lectrostatics

n identical condensers are joined in parallel and are

charged to potential V . Now they are separated and joinedin series. Then the total energy and potential difference ofthe combination will be [MP PET 1993]

(a) Energy and potential difference remain same

(b) Energy remains same and potential difference is nV

(c) Energy increases n times and potential difference is nV

(d) Energy increases n times and potential differenceremains same

Four capacitors of equal capacitance have an equivalentcapacitance Cj when connected in series and an equivalent

capacitance C2 when connected in parallel. The ratio

Q/C 2 is [WB-JEE2009]

(a) 1/4 (b) 1/16

(c) 1/8 (d) 1/12

Five capacitors of IQfjF capacity each are connected to a

d.c. potential of 100 volts as shown in the adjoining figure.

The equivalent capacitance between the points A and B

will be equal to

(a) 40//F

(b) 20//F

(c) 30ff

(d) 10//F

[CPMT 1986,

10VA /^ -v

Wff^\; MP PM

\sWff5/T

~3K~/*10ff

• i nn Ur,u •

12. Three capacitors of capacitances 3/zF, 9//F and 18/zF are

connected once in series and another time in parallel. The

C,ratio of equivalent capacitance in the two cases will

be CPMT 1990; Similar MH CET 2001]

(a) 1 : 15 (b) 15 : 1

(c) 1 : 1 (d) 1 : 3

13. Four condensers each of capacity 4//F are connected as

shown in figure. Vp - VQ = 15 volts . The energy stored in

the system is 4^P [CPMT 1976, 89]

(a) 2400 ergs

(b) 1800 ergs

(c) 3600 ergs

(d) 5400 ergs

14. Two capacitors each of 1//F capacitance are connected in -

parallel and are then charged by 200 volts d.c. supply. The

total energy of their charges (in joules) is

[MP PMT 1990, 2002; J & K CET 2006]

(a) 0.01

(c) 0.04

(b) 0.02

(d) 0.06

15. In an adjoining figure are shown three capacitors Q , C2

and C3 joined to a battery. The correct condition will be

(Symbols have their usual meanings) [CPMT 1988, 89]

16.

17.

"1 Cj^i

HI —^ r^

1 1V3 ' ! Q3

L3

+ 1,-

(a) Q! = Q2 = Q3 and Vj = V2 = V3 = V

(b) Q1=Q2 + Q3andV = \ / 1+V 2+V3

(c) Q, = Q2 + Q3 and V = V1 + V2

(d) Q2 = Q3 and V2 = V3

The equivalent capacitance of the combination shown infigure below is [MP PET 2010]

|C

r(a) 2C (b) C

(d) None of these

Two condensers of capacity 0.3/zF and 0.6/zF respectively

are connected in series. The combination is connected

across a potential of6uo/£s . The ratio of energies stored by

the condensers will be [MP PMT 1990]

(a) i (b) 2

(c) I (d) 4

18. The charge deposited on 4//F capacitor in the circuit is

12V [Kamataka CET 2009]

m..(a) 6x10^0 (b) 12xW* C

(c) 24xlO~6C (d) SexlO^C

19. In given circuit when switch S has been closed then chargeon capacitor A & B respectively [MP PET 2008]

(a)

(c)

A±T

3q, 6q

4.5 q, 4.5 q

' 1T3'

(b) 6q,3q

(d) 5q,4q

21.

22.

23.

25.

26.

Three capacitances of capacity 1 Off, 5//F and 5ff are

connected in parallel. The total capacity will be[MP PET/PMT 1988]

(b) 5ff

(c)

10//F

20/zF (d) None of the above

Three capacitors of capacity Clt C2 C3 are connected in

series. Their total capacity will be[MP Board 1977; MP PET/PMT 1988; CPMT 1996]

(a) Q + C2 + C3 j (b) 1 /(Q + C2 + C3)

(c) (CfJ + €2l + C3 l Tl (d) None of these

Plates of area A are arranged as shown. The distancebetween each plate is d, the net capacitance is

[Orissa JEE 2008]b

(b)

(d) ^pa

Two capacitors connected in parallel having the capacitiesQ and C2 are given ' q' charge, which is distributed

among them. The ratio of the charge on Q and C2 will be

[NCERT 1977; MP PET/PMT 1988]

CLC2

CjC2

(b) -^Li

24. Two capacitors of capacities Q and C2 are charged to

voltages V] and V2 respectively. There will be no exchange

of energy in connecting them in parallel, if [MP PET 1989](a) Cj=C 2

(c)

b) C* \7 = C* '

M t=tFive capacitors, each of capacitance value C are connectedas shown in the figure. The ratio of capacitance between Pand R, and the capacitance between P and Q, is

C [AIIMS 2006](a) 3 :1

(b) 5:2

(c) 2 :3

(d) 1:1A capacitor of capacity Q is charged to the potential of V0.

On disconnecting with the battery, it is connected with acapacitor of capacity C2 as shown in the adjoining figure.

The ratio of energies beforeswitch S will be(a) (Q + C^/q

(b) C j / fQ+Cj j ) C]Vo-L

(c) C,C2

(d) Cj/C2

and after the connection of

1

Tc.

Electrostatics 1021

27. Four capacitors of each of capacity 3ff are connected asshown in the adjoining figure. The ratio of equivalentcapacitance between A and B and between A and Cwill be [Orissa JEE 2011]

A s i B(a) 4:3

29.

31.

32.

(b) 3 :4

(c) 2 :3

(d) 3:2

IL

1T

28. The capacities of two conductors are Q and C2 and their

respective potentials are Vj and V2 . If they are connected by

a thin wire, then the loss of energy will be given by[MP PMT 1986]

/"• y in(b)

2(C,+C2) 2(C1+C2)

2(C1+C2) QC2

A parallel plate condenser is filled with two dielectrics as

shown. Area of each plate is A metre2 and the separation

is t metre. The dielectric constants are /q and k2

respectively. Its capacitance in farad will be[MNR 1985; DCE 1999; AIIMS 2001]

la} 0 n, ,_>, \ ' \ ^2'

(M £°^ 1 + k2

t 2

(c)

£o£l *i K2t 2

30. Three condensers each of capacitance 2F are put in series.The resultant capacitance is

[MP PMT 2001; Similar MP PET 2002; Orissa PMT 2004]

6F (b) |F

(d) 5F

Two condensers of capacities Iff and 2/jF are connected

in series and the system is charged to 120 volts . Then the

P.O. on Iff capacitor (in volts) will be [MP PMT 1987]

(a) 40 (b) 60(c) 80 (d) 120Four condensers are joined as shown in the adjoining figure.The capacity of each is 8//F. The equivalent capacity

between the points A and B will be

(a) 32/zF

(b) 2ff

(c)

(d) I6ff

_l L -! I'- ll nl ' i HI

1022 Electrostatics

34.

35.

36.

37.

38.

IH

The capacities and connection of five capacitors are shownin the adjoining figure. The potential difference between thepoints A and B is 60 volts . Then the equivalent capacity

between A and B and the charge on 5//F capacitancewill be respectively(a) 44//F;300//C

(b) !6ff;l50fjC

(c) 15//F; 200//C

(d) 4/zF;50//C

Three equal capacitors, each with capacitance C areconnected as shown in figure. Then the equivalentcapacitance between A and B is

[MP PET 1985, 89; Similar Orissa JEE 2009]

39.

SffI i II

f Wff

9ffi ! ii r^ i r1

f

-B

(a)(b)

(d) •

C3CC^3

3C2

1 1 _l I1 1c

1 1i r ~i rc c B

Four plates of the same area of cross-section are joined asshown in the figure. The distance between each plate isd .The equivalent capacity across A and B will be

[Similar MP PMT 2009]

(a)

(b)

(c)3£gA

2d

(d) 3_

In the adjoining figure, four capacitors are shown with theirrespective capacities and the P.O. applied. The charge andthe P.D. across the 4ff capacitor will be

(a) 600//C; 150 volts

(b)

(c)

(d)

300//C; 75 volts

800//C; 200 volts

580//C; 145 volts

T4//F 4/zF

Three identical capacitors are combined differently. For thesame voltage to each combination, the one that stores thegreatest energy is [MP PMT 1995](a) Two in parallel and the third in series with it(b) Three in series(c) Three in parallel(d) Two in series and third in parallel with itTwo capacitors each of capacity 2ff are connected inparallel. This system is connected in series with a thirdcapacitor of 12//F capacity. The equivalent capacity of thesystem will be

[MP PET 1990; MP PMT 1990; Similar MP PMT 1985](b) I3ff

(c) 4//F (d) 3ff

40.

41.

43.

44.

A 4/zF condenser is connected in parallel to another

condenser of 8//F . Both the condensers are then connected

in series with a I2ff condenser and charged to 20 volts .

The charge on the plate of 4ff condenser is[MP PET 1989]

(a) 3.3//C (b) 40//C

(c) SOfjC (d) 240//C

A capacitor having capacitance C is charged to a voltageV . It is then removed and connected in parallel withanother identical capacitor which is uncharged. The newcharge on each capacitor is now [MP PET 1990](a) CV (b) CV/2(c) 2CV (d) CV/4Four capacitors are connected in a circuit as shown in thefollowing figure. Calculate the effective capacitance betweenthe points A and B [J & K CET 2008]

II

C2 = 2/zF

Jl

— O i/P3 — i-.fjrIIII

i,A, TB

(c) 9ff

(b) ^-ffD

(d)

42. Effective capacitance between A and B in the figure shownis (all capacitance are in ff) [KCET 2004]

(a) 21 ff

(b) 23 ff

3 _c — - f f

14

(d) — ff

The resultant capacitance between A and B in thefollowing figure is equal to g^p g^p g^p

(a) Iff A- 1 |—p| "

(b) 3ff2

(c) 2ff

(d) 1.5///F3/zF 3ff 3ff

In the following circuit, the resultant capacitance betweenA and B is 1//F. Then value of C is [IIT 19771

f.i 32,,P c V*7

(b) S/d7

i ^ 23(c) ^7,'

(d) I?,

2/f

TV

"TV 4/zF

45. Two dielectric slabs of constant Kx and K2 have been filled

in between the plates of a capacitor as shown below. Whatwill be the capacitance of the capacitor

[MNR 1985; MP PET 1999; DCE 2002]

46.

47.

50.

C j + K 2

(b)

(c)

2eQA(K1

9 KV 1

2£0A ( Kj2 (K,

+ K2"|xK2J

xK2 l+ K2)

Td/24j/9Q/£

±

"T"|

T

What is the equivalent capacitance between A and B in thegiven figure (all are in farad) [BHU 1997]

»¥(b) — F

13

12

8

HF H

16

71A condenser having a Capacity of 6/zF is charged to 100 Vand is then joined to an uncharged condenser of 14/zF and

then removed. The rati6 of the charges on 6//F and 14//Fand the potential of 6ff will be [MP PMT 1991]

6and 50 volt

14

(c) — and 30 volt14

(b) — and 30 volt6

(d) — and 0 volt6

48. 0.2F capacitor is changed to 600 V by a battery. On

removing the battery, iplate condenser of IF. The potential decreases to

[MNR 1978; MP PET 2002]

(a) 100 volts

(c) 300 volts

49. In the circuit shown in

is connected with another parallel

(b) 120uo/ts

(d) 600uo/ts

the figure, the potential differenceacross the 4.5/zF capacitor is

[MP PET 1992; RPET 2001; BVP 2003; AHMS 2010]

(a) — voltso

(b) 4 volts

(c) 6uo/ts

(d) 8 volts

4.5//F

12V

Minimum number of capacitors of 2ff capacitance each

required to obtain a capacitor of 5//F will be [MP PET 1992](a) Three (b) Four(c) Five (d) Six

56.

Electrostatics 1023^ ^ • : : .;' _ ^rm-uM^snmp^r-^-T

51. The total energy stored in the condenser system shown inthe figure will be [Kamataka GET 2008]

(a) 8//J (b) 16//J

(c) 2//J (d) 4//J

52. A capacitor 4//F charged to 50 V is connected to anothercapacitor of 2ff charged to 100 V with plates of likecharges connected together. The total energy before and after

connection in multiples of (10~2J) is [MP PMT 1992](a) 1.5 and 1.33 (b) 1.33 and 1.5(c) 3.0 and 2.67 (d) 2.67 and 3.0

53. Two capacitors of 3pF and 6pF are connected in series anda potential difference of 5000V is applied across thecombination. They are then disconnected and reconnectedin parallel. The potential between the plates is

[MP PMT 1992](a) 2250V (b) 2222V

(c) 2.25xl06V (d) l.lx!06V54. Two identical parallel plate capacitors are connected in

series to a battery of 100 V . A dielectric slab of dielectricconstant 4.0 is inserted between the plates of secondcapacitor. The potential difference across the capacitors willnow be respectively [MP PMT 1992](a) 50V, 50V (b) 80V, 20V(c) 20V, 80V (d) 75V, 25V

55. Four capacitors are connected as shown in the equivalentcapacitance between the points P and Q is

[MP PET 1983; MP PMT 1992; UPSEAT 1999]

(a) 4//F Iff

(b) ^rff4

(d) %ff\j r

The total capacity of the system of capacitors shown in theadjoining figure between the points A and B is

[Pantnagar 1987; SCRA 1996; MP PMT 2002;2ff Orissa JEE 2009]

(a) Iff A

(b) 2/zF

(c) 3ff

(d) 4//FB ' a <r

2/f

57. The equivalent capacitance between A and B in the figure

is Iff . Then the value of capacitance C is [MP PET 1994]

(a) lAff

(b) 2.5ff

(c) 3.5,«F

(d) 1.2/f

61.

1024 ElectrostaticsA condenser of capacity Q is charged to a potential V0.

The electrostatic energy stored in it is U0 . It is connected to

another uncharged condenser of capacity C2 in parallel.

The energy dissipated in the process is [MP PMT 1994]

c,+c -Uo (b)

(d)

QC1+C -Uo

59. Three capacitors each of 6ff are available. The minimum

and maximum capacitances which may be obtained are

[MP PMT 1994]

(a) 6ff,18juF (b) 3ff,l2ff

(c) 2ff,12ff (d) 2ff,l8ff

60. Four capacitors are connected in a circuit as shown in the

figure. The effective capacitance in //F between points A

and B will be [MP PET 1996; Pb. PMT 2001; DPMT 2003;

Similar RPET 1997]98 2ff I2ff

Hh9

(b) 4

(c) 5

(d) 18

2ffI

I H100 capacitors each haying a capacity of 10//F are

connected in parallel and are charged by a potential

difference of 100/cV. The energy stored in the capacitors

and the cost of charging them, if electrical energy costs108 paise per kWh , will be [MP PET 1996; DPMT 2001]

(a) 107 joule and 300 paise

(b) 5xl06 joule and 300 paise

I(c) 5xl06;ou/e and 150 paise

(d) 107 joute and 150 paise

62. Six capacitors each of capacitance of 2/jF are connected as

shown in the figure. The effective capacitance betweenA and Bis L [Kerala PMT 2008]

(a) 12//F

(c)

(e) 2/3juF

(b) 8/3/f

(d)

63. Two condensers, one of capacity C and the other ofcapacity C/2, are connected to a V-volt battery, as shown

64.

65.

66.

67.

T" I ' .TC/2

The work done in charging fully both the condensers is[CBSE PMT 2007]

(a) 2CV2

(0 fcv2

(b) -

(d) lev/2

In the circuit shown here Q = 6/zF, C2 = 3//F and

battery B = 20V . The switch Sj is first closed. It is then

opened and afterwards S2 is closed. What is the charge

finally on C2 I I ^^

(a) 120//C

C,

s,

(b) SOfjC

(c) 40//C

(d) 20/jC1 ' B = 20V

The effective capacitance between the points P and Q of

the arrangement shown in the figure is [MP PET 1997]1 2/zF

(a)

(b)

(c)

(d)

Iff P^

\

I I ||

2ff 2fF

2ff I f f1 1 1

I I i I5ff

I i

1 1

_J L_i r^ ~i r~9//F 1 ,,P

- s;

A capacitor of capacitance 5//F is connected as shown in

the figure. The internal resistance of the cell is O.Sii . The

amount of charge on the capacitor plate is [MP PET 1997]

(a)

(b)

(c)

(d)

0//C

5fjC

IQfjC

25//C

10.

5ffI 1~l r^

2.5V1,

+1*1

l£i

20.A A A A J

Choose the incorrect statement from the following: Whentwo identical capacitors are charged individually to differentpotentials and connected parallel to each other afterdisconnecting them from the source [MP PET 1997]

(a) Net charge equals the sum of initial charges

(b) The net energy stored in the two capacitors is less thanthe sum of the initial individual energies

(c) The net potential difference across them is differentfrom the sum of the individual initial potential difference

(d) The net potential difference across them equals the sumof the individual initial potential differences

68.

71.

A 10//F capacitor and aj 20//F capacitor are connected in

series across a 200 V supply line. The charged capacitors

are then disconnected frorn the line and reconnected withtheir positive plates together and negative plates togetherand no external voltage |is applied. What is the potentialdifference across each capacitor [MP PET 1997]

(a)

(c)

400V

9

400V (d) 200V

69. Two condensers Q and (£2 in a circuit are joined as shown

in figure. The potential of

V2 . The potential of point

C,

(c)

70. To obtain capa>

point A is Vl and that of B is

D will be [MP PMT 1997]

(b)

(d)

Q+C2

C1+C2

ity from three capacitors of2/jF each, they will be arranged IMP PMT/PET 1998]

(a) All the three in series(b) All the three in paralle

(c) Two capacitors in series and the third in parallel withthe combination of first two

(d) Two capacitors in parallel and the third in series withthe combination of first two

A 10//F capacitor is charged to a potential difference of

50 V and is connected to another uncharged capacitor in

parallel. Now the common potential difference becomes20 volt. The capacitance pf second capacitor is

[MP PET 1999; DPMT 2000; Similar CPMT 1991;MP PET 1992; DPMlt 2001; Similar Orissa JEE 2008]

(a) IQjuF

(c) SOfjF

72. What is the effective capacitance between points X and Y

(b)

(d)

20/zF

15//F

[CBSE PMT 1999; Similar AIIMS 2002]C, = 6ff

'a) 24/zF

(b) 18//F

(c) 12//F

(d) 6ff

73. The combined capacity of the parallel combination of twocapacitors is four times jtheir combined capacity whenconnected in series. This mi'ans that [EAMCET 1994]

(a) Their capacities are equal

'JF and 2ff

and Iff

(b) Their capacities are

(c) Their capacities are 0.

(d) Their capacities are infinite

Electrostatics 1025ii.

74. The charge on a capacitor of capacitance WfjF connected

as shown in the figure is [AMU 1995]

(a) 20//C

(b) 15//C

(c) 10//C

(d) Zero

75. The resultant capacitance of given circuit is [RPET 1997]

(a) 3C I 1 *P

(b) 2C

(c) C

76.

2C T

1T T

2C

ABC 12V

^Q

Three plates A, B, C each of area 50 cm2 have separation

3mm between A and B and 3mm between B andC The energy stored when the plates are fully charged is

[SCRA 1996]

(a) 1.6xlO~9J

(b) 2.1xHT9J

(c) 5xKT9J

(d) 7xlO~9J

77. A capacitor of 20ff is charged to 500 volts and connected

in parallel with another capacitor of IQjuF and charged to200 volts . The common potential is [BHU 1997, 2004;

MH CET 1999; CBSE PMT 2000; Similar BHU 2002]

(a) 200uo/ts (b) 300 volts

(c) 400uote (d) 500 volts

78. In the given network capacitance, Cl =10//F, C2 =5juF

and C3 = 4// F . What is the resultant capacitance between

A and B [Pb. PMT 1999; RPMT 2005; MP PET 2006]

(a, 2.2.F A—^X £X

(b) 3.2//F —i—

(c) 1.2//F

(d) 4.7//F

79. The equivalent capacitance between A and B is

T

Iff Iff [RPMT 1999]

(a) 2//F

(c) 5/yF

Iff

(b) 3//F

(d) 0.5//F

1026 Electrostatic

81.

82.

84.

85.

86.

The capacitance between the points A and B in the givencircuit will be FAMU (Med.\: MH CET 1999:[AMU (Med.) 1999; MH CET 1999;

Pb. PET 2002; BCECE 2005]

circuit will be

(a) 1//F

(b) 2//F

(c) 3//F

(d) 4"F I l.5ff

The equivalent capacitance of three capacitors ofcapacitance Cj, C2 and C3 are connected in parallel is 12

units and product Cj.C2.C3 =48 unit. When the capacitorsCj and C2 are connected in parallel, the equivalentcapacitance is 6 units. Then the capacitances are

[KCET 1999](a) 2 ,3 ,7 (b) 1.5,2.5,8(c) 1,5,6 (d) 4,2.6In the circuit shown in figure, each capacitor has a capacityof 3ff . The equivalent capacity between A and B is

[MP PMT 2000; WB-JEE 2010]

87. A 10 ff capacitor is charged to a potential difference of1000 V. The terminals of the charged capacitor aredisconnected from the power supply and connected to theterminals of an uncharged 6/zF capacitor. What is the finalpotential difference across each capacitor [Kerala PMT 2005]

(a) 167V (b) 100 V

(c) 625V (d) 250V

88. Two capacitors A and B are connected in series with abattery as shown in the figure. When the switch S is closedand the two capacitors get charged fully, then

[MP PET 2000]-•-

B

7( \* r~a) -ff

4

(b) 3ff £ .

(c) 6//F

(d) 5ff

H- -i

89.

83. What is the effective capacitance between A and B in thefollowing figure [AMU (Engg.) 2000]

2ff

(b) 2//F

(c) 1.5//F

(d) 2.5//F A d

A potential difference of 300 volts is applied to acombination of 2.0/zF and 8.0//F capacitors connected in

10 V

(a) The potential difference across the plates of A is 4V andacross the plates of B is 6V

(b) The potential difference across the plates of A is 6V andacross the plates of B is 4V

(c) The ratio of electrical energies stored in A and B is 2 : 3

(d) The ratio of charges on A and B is 3 : 2

In the figure, three capacitors each of capacitance 6 pF are

connected in series. The total capacitance of thecombination will be [MH CET 2000; CPMT 2001]

(a) 9xKT12F

(b) 6x]Q-1 2F

(c) 3xlO-12F

(d) 2xlO~1 2F

L-] Oo C^Q

Hi \\h

series. The charge on the l.Qff capacitor is [MP PMT 2000] 90. Equivalent capacitance between A and B is [DCE 2001]

(a) 2.4xHT4C

(c) 7.2x10^ C

(b) 4.8xlO~4C

(d) 9.6xlQ-4CTen capacitor are joined in parallel and charged with abattery up to a potential V. They are then disconnected frombattery and joined again in series then the potential of thiscombination will be [RPET 2000]

(a) 8/1 F

(b) 6//F

(c) 26 //F

(a) V(c) 5V

(b) 10V(d) 2V

In the circuit here, the steady state voltage across capacitorC is a fraction of the battery e.m.f. The fraction is decidedby

(a)

(b)

(c)

only

and R2 only -A-

[ and R3 only

(d) R j , R2 and R3

[AMU (Engg.) 2000]

91. Four identical capacitors are connected as shown indiagram. When a battery of 6 V is connected between A andB, the charge stored is found to be 1.5 fjC. The value of Cl

is AT [Kerala PMT 2005]

(a) 2.5 ff

(b) 15 ff

(c) 1.5 ff

(d) 0.1 ff

92. A parallel plate capacitor with air as the dielectric hascapacitance C. A slab of dielectric constant K and having thesame thickness as the separation between the plates isintroduced so as to fill ohe-fourth of the capacitor as shownin the figure. The new capacitance will be

[Kamataka CET 2007]

93.

94.

95.

96.

(c) (*?+!)•£

(b) (K + 2) —

<«>fThree capacitors of capacitance 3/jF. 10//F and 15/zF areconnected in series to a voltage source of 100V. The chargeon 15 f f is [Pb. PMT 1999; AHMS 2000; CPMT 2001;

Similar MP PMT 1996; RPMT 1999; Pb. PMT 2001](a) 50 fjC (b) 100//C(c) 200/XT (d) 280/A:Consider a parallel plate capacitor of 10//F (micro-farad)with air filled in the gap Between the plates. Now one half ofthe space between the plates is filled with a dielectric of

K = 4

dielectric constant 4, as s hown in the figure. The capacity ofthe capacitor changes to [AFMC 2001; MP PET 2001]

(a) 25 ff

(b) 20 ff

(c) 40 f f

(d) 5/zF

The combination of caplacitors with Cj = 3fi F, C2 = 4// F

and C

Consider the following statements

3 = 2ju F is charged by connecting AB to a battery.

I. Energy stored in C = Energy stored in C2 + Energy

II.III.

stored in C3

Charge on Cj = Charge on C2 + Charge on C3

Potential drop acros s G! = Potential drop across C2 =Potential drop across C3

Which of these is/are correct

(a) I and II

(b) II only

(c) I and III

(d) HI only

Two capacitors

[AMU (Med.) 2001]C3

A-Jh

= 2,iF and C2=6//F in series, are

connected in parallel tola third capacitor C3 =4//F . This

arrangement is then cornected to a battery of e.m.f. = 2V,as shown in the figure. How much energy is lost by thebattery in charging the capacitors

(a) 22xHTbJ

[MP PET 2001]

C, C,

(b) l lx lO~ 6 J— I I I f —

C3

(d) 2V

97. A 20F capacitor is charged to 5V and isolated. It is thenconnected in parallel with an uncharged 30F capacitor.The decrease in the energy of the system will be

[EAMCET 2001]

(a) 25 J (b) 200 J

(c) 125 J (d) 150 J

98. A parallel plate capacitor has capacitance C. If it is equallyfilled with parallel layers of materials of dielectric constantsKj and K2 its capacity becomes Cl. The ratio of Cl to C is

[MP PMT 2001]

(a) (b)

(d)

-K

99 Two identical capacitors each of capacitance 5 //F arecharged to potential 2 fcV and 1 kV respectively. The -veends are connected together. When the +ve ends are alsoconnected together, the loss of energy of the system is

[Kamataka CET 2007]

(a) 160 J (b) OJ

(c) 5J (d) 1.25J

100. The equivalent capacitance between A and B is

—I [Pb. PMT 2002]

c c cHMh-If

B—(a) C/4 (b) 3C/4

(c) C/3 (d) 4C/3

101. The effective capacity between A and B in the figure given is

3//F [Kerala PMT 2002]

I Ih2ff 3/uF

(0

43

12

. jfcG=

24(b) -

(d.

102. An electric field is spread uniformly in Y-axis. Consider apoint A as origin point. The co-ordinates of point B areequal to (0, 2) m. The co-ordinates of point C are (2, 0) m.At points A, B and C, electric potentials are VA, VB and Vc

respectively. From the following options, which is correct

[Gujarat CET 2007]

(a)

(c)

(b)

(d) = VC>VB

103. Two capacitors Cl and C2 = 2C1 are connected in a circuitwith a switch between them as shown in the figure. Initiallythe switch is open and C\s charge Q. The switch isclosed. At steady state, the charge on each capacitor will be

[Orissa JEE 2002]

„ Q. 2Q Ql I C>

(b) Q/3, 2Q/3

(c) 3Q/2, 3Q

(d) 2Q/3, 4Q/3C2 =

104. Three capacitors of 2fjF, 3ff and 6/f are joined in seriesand the combination is charged by means of a 24 voltbattery. The potential difference between the plates of the6/jF capacitor is

(a) 4 volt

(c) 8 volt

[MP PMT 2002]

(b) 6 volt

(d) 10 volt

105. Two capacitors of capacitances 3//F and 6juF are charged

to a potential of 12 Veach. They are now connected to eachother, with the positive plate of each joined to the negativeplate of the other. The potential difference across each willbe [KCET 2002]

(a) 6 volt

(c) 3 volt

(b) 4 volt

(d) Zero

106. Two identical capacitors, have the same capacitance C. Oneof them is charged to potential Vl and the other to V2 . The

negative ends of the capacitors are connected together. Whenthe positive ends are also connected, the decrease in energyof the combined system is

[IIT-JEE (Screening) 2002; Similar KCET 2007]

-V22)

(c) 4c(vi-vz)

(b) 4

(d) lc(V1+V2)2

107. In a given network the equivalent capacitance between Aand B is [Q = C4 = 1 ff, C2 = C3 = 2//F] [MP PET 2007]

( a ) 3 f f

(b) 6ff

(c) 4.5 ff

(d) 2.5/zF

108. A gang capacitor is formed by interlocking a number of platesas shown in figure. The distance between the consecutive platesis 0.885 cm and the overlapping area of the plates is 5 cm2.The capacity of the unit is [Kamataka CET 2006]

(a) 1.0

(b) 4pF

(c) 6.36 pF

(d) 12.72 pF

109. The charge on any one of the 2//F capacitors and 1//F

capacitor will be given respectively (in n C ) as

2flP,(a) 1,2

(b) 2,1

(c) 1,1

(d) 2,2

110. When two identical capacitors are in series have 3/uFcapacitance and when parallel 12//F. What is thecapacitance of each [DPMT 2002]

(a) 6//F (b) 3juF

(c) 12//F (d) 9//F

111. In the circuit as shown in the figure the effective capacitancebetween A and 6 is [KCET 2003]

112. Four equal capacitors, each of capacity C, are arranged asshown. The effective capacitance between A and B is

c [MP PET 2003]

(a)

(0 f C

(b)

(d) C

113. In the figure shown, the effective capacitance between thepoints A and B, if each has capacitance C, is

[MP PET 2003]

114. Three capacitors each of capacity 4//F are to be connected

in such a way that the affective capacitance is 6 // F . This

can be done by [CBSE PMT 2003; Similar MP PET 1989]

(a) Connecting them in parallel

(b) Connecting two in series and one in parallel

(c) Connecting two in parallel and one in series

(d) Connecting all of them in series

115. Three capacitors of capacitance 3//F are connected in a

circuit. Then their maximum and minimum capacitances will[RPET 2003]

(b) 8 / /F , 2//F

(d) 3//F, 2//F

be

(a) 9/ /F, 1//F

(c) 9 / /F , 0//F

116. A capacitor of capacity Ci is charged upto V volt and then

connected to an uncharged capacitor of capacity C2 . Then

final potential difference across each will be

[MP PET 2000; CBSE PMT 2002; MP PET 2003]

C2V+CZ

j +C2

(b)

(d) 1 V

117. A series combination of three capacitors of capacities1//F,2//F and 8//F isjconnected to a battery of e.m.f. 13

volt. The potential difference across the plates of 2//F

capacitor will be [MP PET 2003; Similar DCE 2003]

(b) 8VIV

4V (d) f V

118. Two capacitors of capacitance 2/f and 3//F are joined in

series. Outer plate first capacitor is at 1000 volt and outerplate of second capacitor is earthed (grounded). Now thepotential on inner plate ol

(a) 700Vo/t

(c) 600Voft

each capacitor will be

[MP PMT 2003]

(b) 200Vo/t

(d) 400Vo/t

119. In the figure a potential of + 1200 V is given to point A andpoint B is earthed, what is the potential at the point P

4ff [MP PMT 2004]

B

(a) 100 V

(c) 400V

2ff

(b) 200V

(d) 600V

Electrostatics 1029

120. All six capacitors shown are identical, Each can withstandmaximum 200 volts between its terminals. The maximumvoltage that can be safely applied between A and B is

[MP PMT 2004]

(a) 1200V (b) 400V

(c) 800V (d) 200V

121. The charge on 4 /zF capacitor in the given circuit is .... in //C

[Kerala PMT 2004; Similar Kerala PMT 2006]

(a) 12

(b) 24

(c) 36

(d) 32

«F

3ff

I I

LfU

5ff

-HI-I r^

I ,'10V

122. Three plates of common surface area A are connected asshown. The effective capacitance will be [Orissa PMT 2004]

(a, M (b)

(d)

123. The equivalent capacitance between A and B as shown inthe figure is [Orissa JEE 2010]

.A'

(a)853

|i — — jry ^u/jj

110 V | ^Qff

B

(b) 30/zF

(c) (d) 75 ff

124. All capacitors used in the diagram are identical and each isof capacitance C. Then the effective capacitance betweenthe points A and B is [Kamataka CET 2010]

1

a) 1.5C

c) C

I 1 _i i:si i i rH i 1 11 1 r^

(b) 6C

(d) 3C

1 1

125. n identical capacitors each of capacitance C when

connected in parallel give the effective capacitance 90 /.F

and when connected in series give 2.5 f f . Then the values

of n and C respectively are

(a) 6 and 15 ff

(c) 15 and

[J & K GET 2010]

(b) 5 and 18 ff

(d) 18 and 5 ff

126. The number of ways one can arrange three identicalcapacitors to obtain distinct effective capacitances is

[J & K CET 2010]

(b) 6

(c) 4 (d) 3

127. Three capacitors are connected in the arms of a triangleABC as shown in figure 5 V is applied between A and B.The voltage between B and C is [Kerala PET 2010]

(a) 2 V

(c) 3V

(e) 0.5V

128. A slab of material of dielectric constant K has the same areaas the plates of a parallel plate capacitor but has a thickness

— d. where d is the separation of the plates. The ratio of41

the capacitance C (in the presence of the dielectric) to the

capacitance C0 (in the absence of the dielectric) is

(a)

(c)

3K

K + 3

[AMU (Med.) 2010]

(b)

(d)

K

K

129. The equivalent capacitance between A and B is (in ju F )

[Kerala PMT 2010]3//F 3uF

Am

i

1 1

_iu

1 1n r

_|L_

3ff 3ff

(a) 25

(c) 9

(e) 1

130. A network of four capacitors of capacities equal toCj = C, C2 = 2C, C3 = 3C and C4 = 4C are connected to a

battery as shown in the figure. [AIIMS 2010]

—II—

' 'VThe ratio of the charges on C2 and C4 is

1 *;(c)

131. The potential difference between A and B is

6V [OrissaJEE2011]

1T

3/xF

^r—16V

(a) 13.2V

(c) -6V

(b) -13.2V

(d) 6V

BTwo equal negative charge - q are fixed at the fixed points(0, a) and (0, -a) on the Y-axis. A positive charge Q isreleased from rest at the point (2a, 0) on the X-axis. Thecharge Q will [IIT 1984; Bihar MEE 1995; MP PMT 1996;

Similar DCE 2006]

(a) Execute simple harmonic motion about the origin

(b) Move to the origin and remain at rest

(c) Move to infinity

(d) Execute oscillatory but not simple harmonic motion

An electric line of force in the xy plane is given by equation

x2 + y2 = 1 . A particle with unit positive charge, initially at

rest at the point x = 1, y = 0 in the xy plane [IIT 1988]

(a) Not move at all

(b) Will move along straight line

(c) Will move along the circular line of force

(d) Information is insufficient to draw any conclusion

A positively charged ball hangs from a silk thread We put apositive test charge q0 at a point and measure F / q0 , then

it can be predicted that the electric field strength E

[CPMT 1990]

(a) > F / q 0 (b) = F/q0

(c) < F / q0 (d) Cannot be estimated