electromagnetism 1

In this module we are going study about

• Magnetic fields produced by currents

• Ampere’s Law and Biot-Savart law

• Motion of a charged particle in magnetic field

• The force on a current in a magnetic field

• The torque on a current carrying coil

• Galvanometer, Ammeter and Voltmeter

Electromagnetism-I

Success through conceptual learning

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RK Electromagnetism-I

1

ELECTROMAGNETISM - I

Sources of magnetic field : 1. The first magnetic phenomena observed were those associated with naturally occurring magnets

fragments of iron ore found near the ancient city of magnesia (whence the term “magnet”). These natural magnets attract unmagnetized iron, the effect is most pronounced at certain regions of the magnet known as its poles.

2. In the year 1819, Danish scientist H.C. Oersted observed that a pivoted magnet (a compass needle) was deflected when in the neighborhood of a wire carrying current. Twelve years later Michael Faraday found that a momentary current existed in a circuit while the current in a nearly circuit was being started or stopped. Shortly afterward it was discovered that motion of magnet toward or away from the circuit would produce the same effect.

3. The work of Oersted demonstrated that magnetic effect could be produced by moving electric charges and that of Faraday and Henry showed that currents could be produced by moving magnets.

4. The magnetic field : a) An electric charge sets up or creates an electric field E

in the space surrounding it.

b) The electric field E

exerts a force F Eq=

on a charge q placed in the field.

Similarly

a) A moving charge or a current sets up or creates a magnetic field in the space surrounding it.

b) The magnetic field exerts a force on the moving charge or current carrying conductor in the field.

5. A static charge produces only electric field but moving charge produces both electric field and magnetic field in space.

6. Moving charge current is the source of magnetic field.

7. Magnetic field of a moving charge :

The magnetic field due to moving charge q is 02

qv sinB

4 r

µ θ=π

.

Where v is velocity of charge, r is distance from charge, θ is angle between v

and r

.

02

ˆq v rB

4 r

µ ×=π

The direction of B

is perpendicular to plane containing v

and r

. 8. Ampere established relationship between the current in the conductor and strength of the

magnetic field around the conductor.

9. Oersted’s experiment : A magnetic compass needle placed in the vicinity of a conductor carrying conductor aligned perpendicular to the conductor.

10. The direction of deflection of north pole of magnetic needle is given by Ampere’s swimming rule.

11. Ampere’s swimming rule : Imagine that a man is swimming along the conductor in the direction of the current facing a magnetic needle the north pole of the needle will deflect towards his left hand.

S N

i

q

v

B

r θ


2

12. The magnetic lines of force around a current carrying conductor are concentric circles with their center lying on the conductor.

13. The direction of magnetic field around the current carrying conductor is given by

a) Maxwell’s cork screw rule b) Right hand thumb rule

Maxwell’s cork screw rule : Imagine a right hand screw is advancing in the direction of current in a conductor. Then the direction of rotation of the screw gives the direction of magnetic lines of induction.

Right hand thumb rule : Imagine that a current carrying conductor is held in the right hand palm such that the direction of current is indicated by the thumb. Then the other fingers indicate the direction of magnetic lines of induction.

14. Ampere’s law : Ampere’s law states that the line integral of dl.B

along a closed

path round the current carrying conductor is equal to µ0i where i is the current through the surface bounded by the closed path and µ0 permeability of free space.

idl.B oµ=∫

ir2B oµ=π

r2

iB o

πµ

=

15. Biot-Savart’s law : The magnetic induction at a point near a current carrying conductor is directly proportional to the length of the conductor, the strength of the current and sine of the angle made by the line joining the point with the conductor and inversely proportional to the square of the distance of the point

o o2 3

i.dl.sin idB . ; dB . d lxr

4 4r r

µ µθ= =π π

The direction of magnetic induction is given by the vector (d i rc)×

. This

law is valid only for small current segments.

i

i rB

dl

(b) Right hand thumb rule. Thumb shows the direction of current and curled fingers show the direction

of lines of induction

↑ i

B i

(a) The direction of lines of induction around a current

carrying conductor (Right Hand Screw Rule)

dB C

P

r

Q

i

θ d


3

16. Ampere's law and Biot-Savart law are equivalent but Ampere's law is more useful in some symmetrical conditions.

17. The magnetic induction at a point P due to a conductor of finite length is

)sin(sinr4

iB 0 β+α

πµ

=

18. The magnetic field induction due to the current carrying conductor of infinite

length is given by r2i

Borri2

4B 00

πµ=⋅

πµ=

Magnetic field at one end of infinite long conductor is B = r4i0

πµ

19. The magnetic field induction at a point along the axis of a circular coil is

2/322

20

)xr(

nir24

B+π⋅

πµ=

where n = number of turns, i = current in

the coil, r = radius and x = the distance of the point from the centre of the coil.

2/3220

)xr(

niA24

B+

⋅π

µ=

If x >> r, then 3

0

x

niA24

B ⋅π

µ=

i.e., 3

0

x

M24

B ⋅π

µ=

where M = magnetic moment of the current loop.

20. (a) The magnetic field induction at the centre of a circular coil of n turns is given by relation

rni

2B 0 ⋅

µ=

(b) Magnetic field induction at the centre of an arc is B = 0i

4 r

µ απ

Ex-1 . An equilateral triangular loop of edge d carries a current i. Determine the magnetic field induction at its centroid.

Sol. The loop can be considered to be made up of three straight wires AB, BC and CA, each of length d and carrying a current i as shown in figure.

Let us first find the magnetic induction B1 due to the wire AB at the centroid O.

Here, a = OM = 1 1 d

(CM) dcos3 3 6 2 3

π⎛ ⎞= =⎜ ⎟⎝ ⎠

and θ1 = θ2 = 3π

.

Using equation 0 1 2i(sin sin )B

4 a

µ θ + θ=π

,

B = 0 iB sin sin

4 3 3(d/ 2 3)

µ π π⎛ ⎞= +⎜ ⎟π ⎝ ⎠

= 0 6i4 d

µπ

directed into the plane of the page.

B r

i

A

B

r β α P

i

α

i

B

x

r i

2 2r x+

I

A

I

I

π/3 π/3

π/6 O

d B C


4

Similarly, the magnetic inductions at O due to the wires BC and CA are also 0 6i4 d

µπ

each directed

along the inward normal to the plane of the page.

∴ The net magnetic field induction at O is

B = 3B1 = 09 i

2 d

µπ

.

Ex-2. For the wire PQRST shown in figure, find the magnetic induction B at the point O.

Sol. The entire wire can be divided into four parts as PQ, QR, RS and ST. Obviously, the magnetic

fields due to each portion, at O is directed toward the inward normal to the plane of page. It remains for us to determine the field inductions B1, B2, B3 and B4 corresponding to the four parts respectively and add them to get the resultant field induction B.

Making use of equation 0 i(1 sin )B

4 a

µ − θ=π

B1 = B4 = 0 i1 sin

4 4(d/ 2)

µ π⎡ ⎤−⎢ ⎥π ⎣ ⎦

Making use of equation 0 isinB

4 a

µ θ=π

B2 = B3 = 0 isin( / 4)B

4 d

µ π=π

= 0 i4 d 2

µπ

∴ B = 2(B1 + B2) = 0 2i 12

4 d 2

µ ⎡ ⎤+⎢ ⎥π ⎣ ⎦

B = 03 i

2 2 d

µπ

.

21. For a solenoid of finite length at any point on the axis

B = ]sin[sin2

Ni0 β+αµ

N is number of turns per unit length.

22. A solenoid consists of closely wounded helical coil. Inside the solenoid the field is almost uniform.

The magnetic induction at the centre of the solenoid is l

niB 0µ

=

where l is the axial length and n

is total number of turns in length l of the solenoid. The equation holds good only when the radius of the turns is very small when compared with the length.

23. When current is passed through a helical spring, it contracts due to mutual attraction between consecutive turns.

24. Magnetic field at a point due to a cylindrical current carrying wire

Case (A) : When the wire is solid

Consider a solid cylindrical wire of radius R carrying a current I distributed uniformly across its cross-section. Let P be a point distant r from the axis, where the magnetic field induction B

is to be determined.

α β R

L

+∞ S

i d

i

R

Q P

O

i

T – ∞

M Q P

O

– ∞

π/4 d/√2

I d

B O

R

P r


5

We consider a circular arc of radius r coaxial with the wire, such that the former passes through point P. From symmetry B

must be tangential at each point on the curve and should also

be equal in magnitude. Application of Ampere’s law I 0B d i⋅ = µ∫

yields,

B(2πr) = µ0 i

where i is the current embraced by the closed circular arc. The following two cases arise.

i) When P lies within the cross-section of the wire, i.e., r < R :

Obviously, I

I22

2

r ri

RR

π ⎛ ⎞= = ⎜ ⎟⎝ ⎠π

∴ B(2πr) = µ0 I2

rR

⎛ ⎞⎜ ⎟⎝ ⎠

or, B = 0 I2

ri

2 R

µ=

π. …(i)

ii) When P lies outside the cross-section of the wire, i.e., r > R :

Obviously, i in this case will be I.

∴ B(2πr) = µ0I

or, B = 0I

2 r

µπ

. …(ii)

It is evident that, at the surface of the wire r = R. Both equations (i) as well as (ii) yield consistent and expected results, viz.,

B = 0I

2 r

µπ

Figure displays graphically the variation of B with distance r from the axis.

Case (B) : When the wire is hollow and thin walled

As discussed above, with the same reasoning and using Ampere’s law it is easy to see that

B = 0 (within the wire)

and B = 0I

2 r

µπ

(outside the wire)

The variation of B and r is shown graphically in figure.

Ex-3. A straight wire of circular cross-section of radius R carries a total current I distributed in such a manner that j varies directly as distance form the axis. Find the magnetic field induction B at a distance r from the axis (where r < R).

Sol. Let P be the point where B is to be determined. We draw a circle of radius r coaxial with the wire so that P lies on it. Next, we consider a circular strip of infinitesimally small thickness dr. Current flowing through this strip is

dI = j(2πrdr) = (kr) (2πrdr) where k is a constant

or, Total current I = R 3

2

0

2 kR(k2 )r dr

3ππ =∫ .

∴ k = 3

3I

2 Rπ.

0I2 Rµπ

B

O R r R r

0I2 Rµπ

B

O R r R r

R

I P d

I

d

B O

R

P r

dr


6

Applying Ampere’s law, yields

0B dl i⋅ = µ∫

i = r 3

30

3Ir r2 dr I

R2 R

⎛ ⎞ ⎛ ⎞π = ⎜ ⎟⎜ ⎟⎝ ⎠π⎝ ⎠∫

∴ B(2πr) = µ0

3r

IR

⎛ ⎞⎜ ⎟⎝ ⎠

B = 2

03

r I

2 R

µπ

.

25. The magnetic field induction due to the long current carrying cylindrical conductor is

20

)rR(

ir2

B+

⋅π

µ=

Where R is the radius of the conductor and r is the distance of the point from the surface of the conductor at which the value of B is given. However if r >> R, then

r2i

B 0

πµ=

26. Force on a moving charge :

27. An electric charge moving in a uniform magnetic field experiences a force (F).

F q(v x B)=

or F qvBsin= θ

28. The direction of force is obtained by right hand grip rule. When the charge enters into a uniform magnetic field perpendicular to its direction, then F = qvB. If it enters along the direction of the field, F = 0.

29. The force can only change the direction in which the charge is moving but not its speed. Hence no work is done by it.

30. When a charged particle moves in a uniform magnetic field at right angles to the direction of the field.

i) the trajectory of motion changes and

ii) the speed and energy of a particle remain the same.

31. When a charged particle moves in an electric field, work is done and hence its kinetic energy increases.

32. If we assume that the earth’s magnetic field is due to a long circular loop of current in the interior of the earth, then the plane of the loop will be east-west and the current passes in clockwise direction when seen from earth’s north pole.

33. An electron is moving vertically downwards at a certain place. The direction of force on it due to the horizontal component of the earth’s magnetic field is towards west.

q

v B

Fmax = q v B

+q B

v


7

34. The force acting on a charged particle when it enters a uniform magnetic field of induction B, with velocity v at right angles to the field will provide the necessary centripetal force and make the charged particle move along a circular path of radius ‘r’.

F = qvBr

mv2= ;

mqB

rv

orqBmv

r ==

Since 2

Tπ=

ω, we have

2 mT

qBπ=

Thus time period is independent of the particle-speed. Hence the faster particles move in bigger circles and slower particles move in smaller circles such that the period of revolution T is the same.

35. The frequency m2

qB)(

π=ν and is called cyclotron frequency.

36. If a charged particle enters a uniform magnetic field along the line of the field, it goes undeviated. If it enters at an angle of inclination other than 90° to the field, its path is helical.

37. Helical motion of a charged particle in a uniform magnetic field :

Consider a uniform magnetic field B oriented along x-axis, and a charged particle having a charge q and mass m projected along the X-Y plane, making an angle θ with the X-axis. The component of velocity along the direction of B (i.e., v cos θ) does not contribute to the magnetic force, whereas the component, normal to the direction of B(i.e., v sin θ), contributes for the magnetic force. Thus,

F = qvB sin θ

This provides the necessary centripetal force, for rotational motion, whereas the component of velocity v cos θ, possessed by the particle imparts a movement along the magnetic field. The overall motion is said to be helical, wherein, the particle moves along a spring shaped path (figure).

Notice, that the projection of the path of the particle, in a plane normal to the magnetic field, is a circle (Y-Z plane in the diagram).

The particle rotates about the magnetic field (axis of the helix) with a period of revolution T

given by, 2 m

TqBπ=

which is independent of the speed.

The particle traverses along the magnetic field with a velocity v cos θ; the distance traveled along the helical path axis, in one period of revolution (T) is known as the pitch of the helix (p in the diagram) which is given by

2 mv cosp

qBπ θ= .

It should be noted that the particle started off from the X-Z plane and touches time and again, after each period of revolution (T). Thus, it can be concluded that, the charged particle touches the plane, from where it started, at times t = nT, where n ∈ I.

v

+q

R

B

O

F F

F

F

v v

v

F

v

p

v

θ

+q

B

v cosθ X

Z

Y

v si

n θ

B


8

Ex-4. A magnetic field of induction 0ˆB B i=

exists along the X-axis. A

particle of charge q and mass m is projected from the origin O along the X-Y plane at an angle α to the X-axis with a speed v. (see figure). Find the position coordinates (x, y, z) and the velocity v

of the particle after time t of the projection.

Sol. The initial velocity v of the particle can be expressed as

0ˆ ˆv v(cos i sin j)= α + α

.

The component ˆv cos iα along the magnetic field remains constant as no force acts along B

(ie., X-axis).

Therefore x = (v cos α) t.

Now, the projection of the helical path of the particle on the Y-Z plane (normal to B

) is a circle as shown in figure. The lorentz force (magnetic force) providing the necessary centripetal force is

2m(v sin )

qvBsinR

αα =

where R is the radius of the helix.

or mv sin

RqB

α= .

Also, the angular speed ω for the rotation of the particle about the pitch axis is

2 2 (v sin ) qBT 2 R mπ π αω = = =

π.

∴ The angle rotated about the pitch axis (an imaginary line passing through the centre C and parallel to the X-axis) in time t, is

qBtt

mθ = ω =

Figure shows the projection of the particle’s path; P is the projection of particle at any instant.

The y coordinate is y = PM = R sin θ = mv sin qBt

sinqB m

α ⎛ ⎞⎜ ⎟⎝ ⎠

.

where the sign of sin(qBt/m) automatically takes account all positions of the particle.

The z coordinate is

z = –OM = –(OC – MC)

i.e., z = R(1 – cos θ)

= mv sin qBt

1 cosqB m

⎡ ⎤α ⎛ ⎞− − ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦.

Thus, x = v cos αt, y = mv sin qBt

sinqB m

α ⎛ ⎞⎜ ⎟⎝ ⎠

and z = mv sin qBt

1 cosqB m

⎡ ⎤α ⎛ ⎞− − ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦.

Coming to the velocity of the particle, the component parallel to X-axis remains unchanged.

∴ vx = v cos α.

From figure, the velocity normal to the X-axis, (i.e., in the Y-Z plane) remains constant in magnitude, but has rotated by an angle θ from its initial direction (positive Y-axis).

R

M X

v sin α

–Z

Y

C O

P

θ

v sinα –Z

Y v sinα sinθ

θ

v si

n α

cos

θ

v q

X

Y

α Z B

X

Y

Z

O

R θ C

F F


9

∴ vy = v sin α cos θ = v sin α cos qBtm

⎛ ⎞⎜ ⎟⎝ ⎠

and vz = – v sin α sin θ = –v sin α sin qBtm

⎛ ⎞⎜ ⎟⎝ ⎠

∴ x y zˆ ˆ ˆv v i v j v k= + +

or, qBt qBtˆ ˆ ˆv v cos i sin cos j sin sin km m

⎧ ⎫⎛ ⎞ ⎛ ⎞= α + α − α⎜ ⎟ ⎜ ⎟⎨ ⎬⎝ ⎠ ⎝ ⎠⎩ ⎭

.

38. Motion of a charged particle in space containing both electric and magnetic fields :

If a region contains electric and magnetic fields E

and B

respectively and a particle having a charge q is in motion with a velocity v

, then the force acting on it is given by

F q(E v B)= + ×

known as Lorentz force.

Several cases are possible, depending upon the situation and complexity. Here, we intend to discuss two simple but important (from particle point of view) cases viz, (i) E

is parallel to B

and (ii) E

is perpendicular to B

.

In each case the initial velocity 0v

of particle will be taken normal to both E

and B

.

(i) E

is parallel to B

: Consider a situation in which a constant electric field E

= 0ˆE i and a constant magnetic field 0

ˆB B i=

exist in space pointing along

the X-axis. Let a particle having a charge q and mass m be projected with an initial velocity u the along Y-axis. Let us analyse its further motion.

The case is too simple in the sense that the speed of the particle normal to the direction of E

, (i.e., the velocity u

) remains constant as no work is done on or against it in

the direction. It follows that the particle executes rotatory motion about an axis parallel to the X-axis as a helix due to the magnetic force. However, the electric force qE

keeps on accelerating

the particle which as a result, circulates the helical path once in the same time, but the increasing speed amounts to the pitch of the helix, getting continuously enhanced with time. Thus, the acceleration along X-axis due to electric force is

0xx

qEFa

m m= = .

∴ The velocity vx at time t will be

vx = axt = 0qE t

m.

The initial velocity u (normal to the field) makes the charged particle rotate about the X-axis, as shown in figure. Applying RHR-1 to the particle at origin (initially), it is obvious that the centripetal force (magnetic force) acts along the negative Z-axis. Hence, the projection the helical path on the Y-Z plane will be as shown in the figure. Thus, the velocity components and position coordinates corresponding to the Y-Z plane will be identical to that discussed in Example, with the only substitution of v = u and α = π/2, so that

sin α = 1 and cos α = 0.

y = mu qBt

sinqB m

⎛ ⎞⎜ ⎟⎝ ⎠

z = mu qBt

1 cosqB m

⎡ ⎤⎛ ⎞− − ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

u

–Z

Y

C O

P

θ

Z

u E

X

B

Y

C u

X Z

Y

O


10

vy = u cos θ = u cos qBtm

⎛ ⎞⎜ ⎟⎝ ⎠

and vz = – u sin θ = – u sin qBtm

⎛ ⎞⎜ ⎟⎝ ⎠

.

Using s = 21ut at

2+ along X-axis, where E

produces a constant acceleration, the displacement of

the particle along X-axis is

x = 20qE10 t

2 m⎛ ⎞+ ⎜ ⎟⎝ ⎠

.

∴ The instantaneous position vector of the charged particle can be expressed as :

ˆ ˆ ˆr xi yj zk= + +

2

0qE t mu qBt mu qBtˆ ˆ ˆr i sin j 1 cos k2m qB m qb m

⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + − −⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

0qE t qBt qBtˆ ˆ ˆv i ucos j usin km m m

⎛ ⎞ ⎛ ⎞= + −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

.

(ii) E

is perpendicular to B

: We know venture into the case where 0ˆE E i=

and 0ˆB B j=

, and a

charged particle is released at the origin O. The electric field keeps on accelerating it along the X-axis, while the magnetic field B

(directed along Y-axis) makes the particle rotate in a plane normal to it, (i.e., the X-Z plane). There is no movement along the Y-axis, as neither there is any initial velocity component nor there is any acceleration in that direction. Thus, the overall motion is purely in the X-Z plane.

First of all let us express the velocity at any instant as

x zˆ ˆv v i v k= +

where vx and vz are the components of the velocity along X and Z axis respectively. Net force on the particle at time t is

e mF F F= +

qE q(v B)= + ×

0 x z 0ˆ ˆ ˆ ˆq[E i (v i v k)B j]= + + ,

i.e., 0 z 0 x 0 x zˆ ˆ ˆ ˆF q(E v B )i qv B k F i F k= − + = +

so that Fx = q(E0 – vz B0) and Fz = qvxB0.

∴ The acceleration along X and Z axis will be respectively

xx 0 z 0

F qa (E v B )

m m= = −

and z 0xz

qv BFa

m m= = .

Now, 0 0x zz

qB qBda dv(a )

dt m dt m−⎛ ⎞= = −⎜ ⎟

⎝ ⎠

= 0 x 0qB qv B

m m⎛ ⎞− ⎜ ⎟⎝ ⎠

or, 22

0xx2

qBd vv 0

mdt

⎛ ⎞+ =⎜ ⎟⎝ ⎠

.

This is the differential equation of a SHM whose general solution can be expressed as

vx = v1 sin (ωt + δ)


11

where ω2 = 2

0qB

m⎛ ⎞⎜ ⎟⎝ ⎠

and ; v1 and δ are constants which depend upon a particular situation and

can be obtained by the use of boundary conditions.

Initially, at time t = 0, vx = vy = vz = 0.

∴ 0 = v1 sin (δ) or, δ = 0.

∴ vx = v1 sin ωt

Also, x1 x

dvv cos( t) a

dt= ω ω = .

Again, initially at time t = 0, ax = 0qE

m.

∴ 0qE

m= ωv1 or, v1 = 0qE

mω.

But, ω = 0qB

m ∴ v1 = 0

0

E

B.

∴ vx = 0

0

EB

sin ωt …(i)

Again, from az = zx 0

dv qv B

dt m= .

Substituting for vx, we have

az = 0 zqE dvsin t

m dtω = .

Integrating between the limits t = 0, vz = 0 and t = t and vz = vz,

vz = 0qE(1 cos t)

m− ω

ω …(ii)

Integration of expressions corresponding to vx and vz between the limits, t = 0, vx = 0, vz = 0 and t = t, vx = vx, vz = vz, yields

x = 0

0

E(1 cos t)

B− ω

ω …(iii)

and z = 0

0

E( t sin t)

Bω − ω

ω …(iv)

where ω = 0qB

m. …(v)

Thus, equation (i) and (ii) combinedly give the velocity at any instant while equations (iii) and (iv) yield the position coordinates on the X-Z plane.

The path traveled by the particle is a cycloid. In general, a cycloid is represented by the parametric form :

x = a(θ ± sinθ) and y = a(1 ± cosθ)

where ‘a’ is known as the radius of the generating circle, and 2πa is the base of the cycloid. In our discussion see figure,

a = 0

0

E

B ω.

39. The frequency of a charged particle in a uniform magnetic field is known as cyclotron frequency as the particles in a circular accelerator, called cyclotron, move with this frequency.

40. Cyclotron is a device used to accelerate charged particles to high speed for nuclear reaction. It was invented by Lawrence.

2a

E C

D A

–Z O

X

2πa 2πa


12

41. Force on a current carrying conductor :

42. When a conductor of length l carrying a current i is placed at an angle θ to the direction of the magnetic field of flux density or induction B, the force on the conductor or wire is given by

θ== sinilBFor)Bxl(iF

Its direction can be determined by using Fleming’s left hand rule, whose statement is as follows:

Stretch the fore finger, middle finger and thumb of the left hand mutually perpendicular to each other. If the fore finger represents the direction of magnetic field, the middle finger that of current, then the thumb will represent the direction of force on the conductor.

Ex-5. Figure shows a circular arc ab of radius r carrying a current i resting in a uniform magnetic field of strength B. Find the magnitude and direction of the force (magnetic) exerted on the arc.

Sol. The length of straight line joining ab is

2r sin2θ⎛ ⎞= ⎜ ⎟

⎝ ⎠ .

The required force is

netF i(ab B)= ×

or, netF 2Bir sin2θ⎛ ⎞= ⎜ ⎟

⎝ ⎠.

(in a direction normal to the line joining ab to the right).

43. Force between two current carrying conductors :

If i1 and i2 are the strengths of currents passing through two infinitely long, straight and parallel wires separated by a distance r, the magnetic field induction B, due to the flow of current in the

first conductor at a distance r on the second conductor is r2

iB 10

1 πµ

=

.

The force exerted by this induction on a length l on the second conductor is F = lBi 12

The force per unit length is r2

iiF 210

πµ

=

.

If the current is in the same direction, there will be attraction and if the current is passing in opposite direction, there will be repulsion.

44. An ampere is that steady current when flowing in each of two long straight parallel wires separated by a distance of one metre apart in vacuum causes each wire exert to each other a force of 2 × 10–7 N per each metre length of wire.

F

B

vori

Fleming’s left hand rule

B

i l

i

i

F

B

i

B i

a

r b

θ

r

i1 i2

r


13

Ex-6. A square loop of side a carries a current i2 with a long straight conductor carrying a current i1

lying in the plane of the loop, with its closer edge, which is parallel to the conductor, distant b.

Find the force exerted on the loop.

Sol. The relevant diagram is shown in figure. The magnetic field due to the

conductor is normal to the plane of the square loop. The total force on

the loop can be obtained as the vector sum of the forces on its four

arms, namely pq, qr, rs and sp respectively.

Let the current i2 flow in the loop in the clockwise sense as shown by arrows. Evidently, the relative configurations of the edges qr and ps with

respect to the long conductor are identical and hence the forces on

them will be equal in magnitude; however, the current directions in them being opposite, the

forces cancel each other.

Force on side pq is given by F1 = B1i2 a(sin 90°)

where B1 is the magnetic field at the site of pq, which is equal to 0 1i2 a

µπ

.

∴ F1 = 0 1 2i i

2

µπ

. (toward left)

And, force on the side rs is F2 = B2i2 a sin 90° where B2 is the magnetic field at the location of rs, which is equal to

F2 = 0 1i

2 (a b)

µπ +

∴ F2 = 0 1 2i i a

2 (a b)

µπ +

(toward right)

∴ The net force (toward left) acting on the loop is

Fnet = F1 – F2 = 0 1 2i i b

2 (a b)

µπ +

.

45. Force and torque on current loop or coil in a magnetic field :

The total magnetic force on any closed current loop in a uniform magnetic field is zero.

46. Torque or couple on a current carrying rectangular conductor or

loop in a uniform magnetic field is given by τ = iAB sinθ where A is

the area of the rectangular loop, B is the magnetic induction and θ

is the angle between the normal to the plane of the rectangular loop

and the field. If there are n turns, then the torque acting on the coil

suspended is given by τ = ni AB sin θ or τ = MB sinθ where M is the

magnetic dipole moment equal to niA and θ is the angle between

the magnetic induction and the normal to the plane of the coil i.e., the direction of the magnetic

moment. When the plane of the coil makes an angle θ with the field, then the couple acting on the

coil is

τ = niAB Cosθ or τ = MB cos θ.

i

P

B

Q R

S

i Bil

Bil

θ

i

i

p s

i1

F2

r q

–∞

+∞

⊗

⊗

i2

F1

b a


14

Moving coil galvanometer :

47. A moving coil galvanometer consists of a powerful horse shoe magnet with concave poles to produce a uniform radial magnetic field. On a cylindrical soft iron core, a coil is wound and the coil is suspended with a phosphorbronze fibre. The plane of the coil always lies in the direction of the magnetic field because the magnetic field is radial. The whole apparatus is kept inside a brass case provided with a glass window.

NABC

iθ= ampere

Here C is the couple per unit twist on the suspension fibre, ‘i’ is the current passing through the galvanometer coil and θ is the angle of deflection by the needle.

C/BAN is a constant (k) is called as galvanometer constant. Deflection is measured more accurately using Lamp and Scale arrangement. The ray reflected onto the scale by the mirror is deflected by 'x'. The distance between the mirror attached to the suspension fibre of the galvanometer and the scale is D, then

Tan 2θ ≈ 2θ when 2θ is very small

Then 2Dx

; Dx

2 =θ=θ ; i =2Dx

. BAN

C

48. The current sensitivity of a galvanometer is the deflection in mm produced on a scale kept at a distance of one metre by a constant current of one microampere.

49. The reciprocal of the current sensitivity is called figure of merit and is expressed in µA/mm.

50. A current upto 10–9A can be measured using moving coil galvanometer.

51. Table Galvanometer : It has a rectangular coil of insulated copper supported on two bearings. The poles of the magnet are concave. It has a light aluminium pointer which moves on a scale. The whole arrangement is kept in an ebonite case with a glass window.

52. Tangent Galvanometer :

a) It is portable and minimum measurable current is of the order of 10–6 A.

b) works on the principle of Tangent law B = BH Tanθ

Here B = Magnetic induction due to passage of current in

the coil = r2i0µ

c) current measured by Tangent galvanometer is ⎟⎟⎠

⎞⎜⎜⎝

⎛

µ=

nrB2

i0

H

Tanθ = KTanθ r = Radius of coil

n = number of turns of coil

d) Reading is more accurate when θ = 45° since relative error di 1i sin2

∝θ

and it is minimum

for 45°

e) Sensitiveness is maximum when θ = 0° since sensitiveness didθ ∝ cos2θ, which is maximum

for θ = 0°. f) During experiment, plane of the coil should be along the magnetic meridian [to fulfill the

requirement of tangent law]

i

P

B

Q R

S

b Bil

Bil

θ

i

θ

i B

HB


15

53. Shunt : a) A low resistance connected in parallel to galvanometer to protect it from large current is known

as shunt. b) i = ig + is

c) ( )

SGSi

ig +=

d) ( )

SGGi

is +=

e) n1

SGS

i

i

s

g =+

=

f) effective resistance of circuit = SG

GS+

g) If the range of galvanometer is increased to n times, 1/nth of main current passes through galvanometer. Hence sensitiveness decrease by n times.

54. Ammeter : a) It is a device used to measure current in electrical circuits. b) Galvanometer can be converted in to Ammeter by connecting low resistance parallel to it. c) To increase the range by ‘n’ times or to decrease the Sensitiveness by ‘n’ times, shunt to be

connected across Galvanometer. ( )

( )1nG

igiGig

S−

=−

=

Here n =A/divisionsnewA/sdividisionold

rangeoldrangenew

ii

g

==

d) Resistance of Ammeter = SG

GS+

e) Resistance of ideal Ammeter is zero and its conductivity is infinity f) Ammeter must be always connected in series to the conductor. g) Among low range and high range Ammeter, low range Ammeter has more resistance. h) As shunt value decreases sensitivity decreases, accuracy increases.

55. Voltmeter : a) Voltmeter is a device used to measure P.D. across the

conductor in electric circuits. b) Galvanometer is converted into voltmeter by connecting high

resistance in series to it. c) Voltmeter is always connected in parallel to the conductor

[P.D. across which is to be measured]

d) Resistance of voltmeter = G +R =igV

e) Here ‘V’ is range of voltmeter (e) resistance of ideal voltmeter is infinity and conductivity is zero. f) Among low range and high range voltmeters, high range voltmeter has more resistance. g) P.D. across the ends of voltmeter is, V = ig + (G + R)

h) Resistance to be connected in series to galvanometer to convert into voltmeter is GiV

Rg

−= .

i) To increase the range by n times,

n 1

2

rangeVold

rangeVnew=

( )( )

g

g

i G R R1

i G G

+= ⇒ +

Hence resistance to be connected in series to galvanometer is R = G(n – 1). j) As series resister value increases sensitivity decreases, accuracy increases.

i – ig S

i ig G

i – ig

R

r i

ig

G


16

Assertion & Reason : In each of the following questions, a statement is given and a corresponding statement or reason is given just below it. In the statements, marks the correct answer as 1) If both Assertion and Reason are true and Reason is correct explanation of Assertion. 2) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 3) If Assertion is true but Reason is false. 4) If both Assertion and Reason are false. 5) If Assertion is false but Reason is true.

1. [A] : Magnetic field interacts with a moving charge and not with stationary charge. [R] : A moving charge produces a magnetic field.

2. [A] : A linear solenoid carrying current is equivalent to bar magnet. [R] : The magnetic field lines of both are same.

3. [A] : Force experienced by moving charge will be maximum if direction of velocity of charge is perpendicular to applied magnetic field. [R] : Force on moving charge is independent of direction of applied magnetic field.

4. [A] : Torque on coil is maximum, when coil is suspended in radial magnetic field. [R] : Torque depends upon the magnitude of the applied magnetic field.

5. [A] : The coil is wound over the metallic frame in moving coil galvanometer. [R] : The metallic frame help in making steady deflection without any oscillation.

6. [A] : When two long parallel wires, hanging freely are connected in series to a battery, they come closer to each other. [R] : Wires carrying current in opposite direction repel each other.

7. [A] : When the observation point lies along the length of current element, magnetic field is zero. [R] : Magnetic field close to current element is zero.

8. [A] : A moving coil galvanometer has a permanent magnet with cylindrical pole faces. [R] : The radial magnetic field produced keeps the constant of the galvanometer to be constant throughout the deflection range.

9. [A] : A moving coil galvanometer has a permanent magnet with cylindrical pole faces. [R] : The radial magnetic field produced makes the coil to experience a constant torque in any deflected position.

10. [A] : A moving coil galvanometer has a permanent magnet with cylindrical pole faces. [R] : The radial magnetic field produced makes the calibration of the scale to be uniform throughout the scale.

11. [A] : A soft iron cylinder is arrange in the space of the coil suspended between the pole pieces of the magnet. [R] : To increase the sensitivity of the galvanometer.

12. [A] : The resistance of a voltmeter is high. [R] : The voltmeter is connected always in parallel.

13. [A] : The resistance of an ideal voltmeter is infinite. [R] : When connected the voltmeter should not draw any current from main circuit thus keeping the current in that circuit constant.

14. [A] : The resistance of potentiometer during the measurement of potential differences, can be considered as infinite. [R] : It does not draw any current from secondary circuit.

15. [A] : The resistance of an ammeter is very low. [R] : The ammeter is always connected in series.

16. [A] : The ideal ammeter has zero resistance. [R] : The ammeter is always connected in series. As such it should not alter the current in the circuit.


17

17. [A] : The magnetic field ‘B’ due to a conductor of radius ‘r’ carrying a current ‘i’, at a distance of ‘x’ from the axis of the wire (x<r) is proportional to x. [R] : The current is distributed uniformly along the area of cross-section of the wire.

18. [A] : An electron moves along the line AB which lies in the same plane as a circular loop of conducting wire as shown in the figure current induces in the coil.

[R] : Moving electron produces a magnetic field. As it moves the magnetic field at a point changes.

19. [A] : When a current passing through a coil decreases, back emf is induced in it. [R] : As the current is decreasing the magnetic field produced in the coil decreases.

20. [A] : A Straight and very long wire carries current i. If the wire is vertically placed and carries current in the upward direction, null point will be formed on the west side. [R] : If the wire is horizontal and carries current from west to east, null point will be formed at a point above the conductor.

21. [A] : A vertical straight wire carries a current vertically upwards. Points P and Q lie respectively to the east and west of the conductor at the same distance from it. At P the induction is BP, at Q the induction is BQ, then BP > BQ.

[R] : Two infinitely long thin insulated straight wires carrying currents i and i lie along x and y axes respectively. The locus of the points where the magnetic field is zero is straight line.

22. [A] : Two very long straight wires are connected in series with a battery and are arranged parallel to each other. Then the mutual force between the wires is repulsive. [R] : If the two wires are connected in parallel with the battery and one arranged parallel to each other, the mutual force between wires is attractive.

23. [A] : Moving electric charge produce both electric and magnetic field. [R] : A current carrying conductor produces a magnetic field in the surrounding space.

24. [A] : If a straight conductor carries current normally outwards from the plane of paper, lines of induction are concentric circles in counter clockwise direction. [R] : A Straight conductor carrying current produces a magnetic field, which is radially symmetric.

25. [A] : An infinite long conductor carries a current i. The work done to move a unit north pole round it once is µoi. [R] : A straight cylindrical pipe carries current i, the field inside is zero.

26. [A] : For a given length l of a wire carrying a current i, the number of circular turns which produce the maximum magnetic moment is one. [R] : A current carrying circular coil behaves as a magnetic shell.

27. [A] : When a charged particle moves at right angles to the magnetic field, the momentum of the particle will remain constant. [R] : When a charged particle is moving in magnetic field, work done by the magnetic field on the

charged particle is zero. 28. [A] : When a charged particle enters perpendicular to the direction of a uniform magnetic field in

the time period of rotation depends on nature the particle. [R] : When the particle enters the magnetic field at angle θ (≠0, ≠1800, ≠900), the path of the

particle will be helical. 29. [A] : The force experienced by a semi circular wire radius r when it is

carrying a current i and is placed in a uniform magnetic field of induction B as shown in fig(a) is zero.

[R] : The force experienced by a semi circular wire of radius r when it is carrying a current i and is placed in a uniform magnetic field of induction B as shown in fig(b) is 2B ir.

B

(b)

i

(a)

B i

A B e–


18

30. [A] : If an electron is not deflected in passing through a certain region of space, then there is no electric and magnetic fields.

[R] : When a charged particle moves parallel to electric field its kinetic energy increases. 31. [A] : When a current carrying coil is placed in a uniform magnetic field, the net force on it always

is zero. [R] : The current carrying coil acts like a dipole.

32. [A] : In moving coil Galvanometer, phosphorous bronze wire is used as suspension wire. [R] : Phosphorous bronze has high young’s modulus , less rigidity modules.

33. [A] : For more current sensitivity, of Moving coil Galvanometer, B, A, N should be more and c should be small.

[R] : In moving coil Galvanometer, voltage sensitivity also varies as that of current sensitivity. 34. [A] : In Moving coil Galvanometer, concave shape magnetic poles makes current as linear

function of deflection(θ). [R] : In case of redial magnetic field normal to the plane of coil always makes 90° with magnetic

field. 35. [A] : In Moving coil Galvanometer external magnetic fields have no effect on the deflection.

[R] : In tangent galvanometer external magnetic fields may influence the deflection. 36. [A] : Shunt increases the range of galvanometer.

[R] : Shunt increases the life of galvanometer. 37. [A] : Ammeter must be always connected in series.

[R] : Conductance of ideal ammeter is infinity. 38. [A] : Voltmeter must be always connected in parallel.

[R] : Conductance of ideal voltmeter is infinity. 39. [A] : The resistance of ammeter is less than that of galvanometer.

[R] : In ammeter zero division is at one end of the scale, in Galvanometer zero division is at the middle of the scale.

40. [A] : A beam of charged particles is passed through a magnetic field. The work done on the beam by the field is dependent on the deflection of the beam.

[R] : The time rate of the work done by a magnetic field B

on a charged particle of moving in a helical path is zero.

41. [A] : On increasing length of the, Potentiometer wire, its sensitivity increases. [R] : On increasing length of the Potentiometer wire, potential gradient decreases.

42. To convert galvanometer into an ammeter, a shunt is used. [A] : The accuracy of the meter increases. [R] : The range of the meter increases.

43. To convert a galvanometer into a voltmeter, a large resistance is connected in series with the galvanometer. Due to use of large resistance.

[A] : Accuracy of the voltmeter increases. [R] : Sensitivity decreases.

44. [A] : Range and least count of ammeter and voltmeter are linearly related with each other. [R] : Least count and sensitivity of an ammeter are related inversely with each other.

45. A current i is passing through a circular coil. [A] : To induce magnetic induction of constant magnitude (at centre of the coil), the current

required in it is directly proportional to its radius. [R] : Induction of induced magnetic field at centre is inversely proportional to radius of the coil.

46. [A] : In Meter bridge, meter bridge wire is replaced by another wire having twice the cross sectional area, the accuracy increases.

[R] : Meter bridge works on the principle of wheat stone bridge.


19

47. [A] : If a moving charged particle traces a helical path in a uniform magnetic field, axis of the helix is parallel to the magnetic field.

[R] : If in a region a uniform magnetic field and a uniform electric field both exist, a charged particle moving in this region cannot trace circular path.

48. [A] : In tangent Galvanometer plane of the current carrying coil must be in magnetic meridian.

[R] : When plane of the coil is in magnetic meridian, B

and HB

are perpendicular to each other.

49. [A] : M.C.G can be used for the measurement of currents even in mines. [R] : In case of M.C.G galvanometer constant does not depend on earth’s magnetic field.

50. [A] : A linear solenoid carrying current is equivalent to a bar magnet. [R] : The magnetic field lines of both are same.

51. [A] : Free electrons always keep on moving in a conductor even then no magnetic force act on them in magnetic field unless a current is passed through it.

[R] : The average velocity of free electron is zero. 52. [A] : Torque on the coil is maximum, when coil is suspended in a radial magnetic field.

[R] : Torque depends upon the magnitude of the applied magnetic field. 53. [A] : The coil is wound over the metallic frame in moving coil galvanometer.

[R] : The metallic frame help in making steady deflection without any oscillation. 54. [A] : Out of galvanometer, ammeter and voltmeter, resistance of ammeter is lowest and

resistance of voltmeter is highest. [R] : An ammeter is connected in series and a voltmeter is connected in parallel, in a circuit.

55. [A] : For a point on the axis of a circular coil carrying current, magnetic field is maximum at the centre of the coil.

[R] : Magnetic field is inversely proportional to the distance of point from the circular coil. 56. [A] : A circular loop carrying current lies in XY plane with its centre at origin having a magnetic

flux in negative Z-axis. [R] : Magnetic flux direction is independent of the direction of current in conductor.

57. [A] : The energy of charged particle moving in a uniform magnetic field does not change. [R] : Work done by the magnetic field on the charge is zero.

58. [A] : The electron passing through crossed magnetic and electric field is always deflected from its path.

[R] : If velocity of electron is equal to ratio of electric and magnetic field applied than electron beam remains undeflected.

59. [A] : A small coil carrying current, in equilibrium, is perpendicular to the direction of the uniform magnetic field.

[R] : Torque is maximum when plane of coil and direction of the magnetic fields is parallel to each other.

60. [A] : Earth’s magnetic field does not affect the working of a moving coil galvanometer. [R] : The earth’s magnetic field is quite weak as compared to magnetic field produced in the

moving coil galvanometer. 61. [A] : Soft iron core is used in a moving coil galvanometer.

[R] : Soft iron is ferromagnetic in nature. 62. [A] : In ammeter, current in shunt is always greater than current in galvanometer.

[R] : Value of shunt resistance is negative if current in shunt is less than current in galvanometer. 63. [A] : No net force acts on a rectangular coil carrying a steady current when suspended freely in a

uniform magnetic field. [R] : Forces acting on each pair of the opposite sides of the coil are equal and opposite.

64. [A] : If an electron and proton enter in an electric field with equal energy, then path of electron more curved than that of proton.

[R] : Electron has a tendency to form large curve due to small mass.


20

65. [A] : For a given charged particle moving in a given magnetic field, the radius of circular path is directly proportional to the momentum of particle.

[R] : The effect of magnetic field on a charge particle, change only its path from linear to circular. 66. [A] : If a proton and an α-particle enter a uniform magnetic field perpendicularly, with the same

speed, the time period of revolution of α - particle is double that of proton. [R] : In a magnetic field, the time period of revolution of a charged particle is directly proportional

to the mass of the particle and is inversely proportional to charge of particle. 67. [A] : If an electron while coming vertically from outerspace enter the earth’s magnetic field, it is

deflected towards west. [R] : Electron has negative charge.

68. [A] : The workdone by magnetic field on a moving charge is zero. [R] : In magnetic field force is perpendicular to the velocity.

69. [A] : An electron and proton enters a magnetic field with equal velocities, then the force experienced by proton will be more than electron.

[R] : The mass of proton is 1837 times more than the mass of electron. 70. [A] : A charged particle moving in a uniform magnetic field penetrates a layer of lead and there by

loses half of its kinetic energy. The radius of curvature of its path is now reduced to half of its initial value.

[R] : Kinetic energy is inversely proportional to radius of curvature. 71. [A] : Tangent Galvanometer can not be used in mines.

[R] : In case of Tangent Galvanometer reduction factor depends on earth’s magnetic field.

72. Match the following : List – I List – II a) In MCG e) i α θ b) in tangent galvanometer f) i θα tan

c) Biot Savart’s law g) B=2

o

r

sindli4

θπ

µ

d) Ampere’s law h) B=ri

4o

πµ

1) a-e, b-f, c-g, d-h 2) a-h, b-g, c-f, d-e 3) a-f, b-e, c-h, d-g 4) a-g, b-h, c-e, d-f 73. Match the following :

List – I List – II a) infinite resistance e) ideal voltmeter b) zero resistance f) ideal ammeter c) Lorentz’s magnetic force g) q(VxB) d) at centre of current

carrying circular loop h) B=ri

2oµ

1) a-e, b-f, c-g, d-h 2) a-h, b-g, c-f, d-e 3) a-f, b-e, c-h, d-g 4) a-g, b-h, c-e, d-f 74. Match the following. List – I List – II

a) right hand thumb rule e) magnitude of magnetic field b) Biot-Savart law f) direction of induced current c) Fleming’s left hand rule g) direction of magnetic field d) Fleming’s right hand rule g) direction of force due to magnetic fields The correct code is 1) a-g, b-e, c-h, d-f 2) a-f, b-g, c-h, d-e 3) a-g, b-e, c-h, d-f 4) a-e, b-g, c-f, d-h


21

75. The magnetic inductions due to a circular coil carrying current at its centre, at distances on its axis x = R and x = 2R are represented by BC, BR, B2R. What are the ascending order of these values.

1) BC, BR, B2R 2) B2RBR, BC 3) BC, B2R, BR 4) BR, B2R, BC 76. The resistance of moving coil galvanometer is ‘G’ and that of an ammeter is RA and that of

voltmeter is RV arrange them in decreasing order 1) G > RA > RV 2) RV > G > RA 3) G > RV > RA 4) RA > G > RV

KEY :

1) 1 2) 1 3) 3 4) 2 5) 1 6) 5 7) 2 8) 1 9) 1 10) 1

11) 1 12) 2 13) 1 14) 1 15) 2 16) 1 17) 1 18) 1 19) 1 20) 2

21) 2 22) 2 23) 2 24) 1 25) 2 26) 2 27) 5 28) 2 29) 2 30) 4

31) 1 32) 1 33) 2 34) 1 35) 2 36) 2 37) 2 38) 3 39) 2 40) 5

41) 1 42) 2 43) 2 44) 2 45) 2 46) 5 47) 2 48) 1 49) 1 50) 1

51) 1 52) 2 53) 1 54) 2 55) 1 56) 3 57) 1 58) 5 59) 2 60) 1

61) 1 62) 1 63) 1 64) 4 65) 2 66) 1 67) 1 68) 1 69) 5 70) 4

71) 1 72) 1 73) 1 74) 1 75) 2 76) 2

MULTI CORRECT ANSWERS : 1. Choose the correct statements :

a) The work of Oersted demonstrated that magnetic effect could be produced by moving electric charge.

b) The work of Faraday and Henry demonstrated that magnetic effects could be produced by moving electric charge.

c) The work of Oersted demonstrated that currents could be produced by moving magnets d) The work of Faraday and Henry demonstrated that currents could be produced by moving

magnets. 2. Choose the correct statements :

a) The electric force on a charge does not depend on the speed of the charge b) The electric force on a charge depends on the speed of the charge. c) The magnetic force on a charge does not depend on the speed of the charge d) The magnetic force on a charge depends on the speed of the charge.

3. F = qvBsinθ is the equation of the Lorentz force F on a charge q moving with a velocity v in a magnetic field B. Which of the following pairs of quantities are always perpendicular to each other? a) F – v b) F – B c) v – B d) v – q

4. In which of the following situations, the magnetic field will not exert a force ? a) On a static charge, in the same direction as the direction of the magnetic field b) On a static charge, in a direction perpendicular to the direction of the magnetic field c) On a moving charge, in the same direction as the direction of the magnetic field d) On a moving charge, in a direction perpendicular to the direction of the magnetic field

5. Which of the particles passing normally through a magnetic field will not be affected ? a) Electrons b) Neutrons c) Protons d) Neutrinos

6. A proton is moving in a uniform magnetic field. The initial direction of proton makes an angle θ with the magnetic field. Which of the following pairs representing θ and the path of the proton are correct ? a) θ = 0°–Straight line b) θ = 90°– Straight line c) θ = 90° – Circular d) 0°<θ<90°– Helical


22

7. Both the electric an the magnetic fields can deflect an electron. Choose the correct alternatives. The force exerted by the a) magnetic field changes the kinetic energy of the electron b) magnetic field does not change the kinetic energy of the electron c) electric field changes the kinetic energy of the electron d) electric field does not change the kinetic energy of the electron

8. Which of the following pairs representing the field and the possible path of the deflection of an electron beam in the field are correct ? a) Uniform magnetic field – Circular. b) Uniform magnetic field – Helical c) Uniform magnetic field – Helical. d) Uniform electric field – Parabola

9. A particle (electron or proton) is moving vertically downward through a magnetic field directed from south to north in a horizontal plane. Which of the following pairs representing particle and the direction of deflection of the particle are correct ? a) Electron – West b) Electron – East c) Proton – West d) Proton – East

10. Choose the correct statements : a) The magnetic lines of force always emanate from the north pole, follow a curved path and end

at the south pole. b) The magnetic lines of force always emanate from the south pole and reach back the north

pole moving inside the magnet. c) Near the magnetic poles, the lines of force are closer. d) Near the magnetic poles, the lines of force are farther.

11. At any place, the lines of force in earth’s magnetic field are a) Parallel b) Perpendicular c) equidistant d) at different distances

12. A positively charged particle (+q) of mass m enters a uniform magnetic field B with a velocity v perpendicular to the filed. The particle traverses a circular path. The radius of this circular path depends a) linearly on the mass of the particle b) inversely on the mass of the particle c) linearly on the charge of the particle d) inversely on the charge of the particle

13. A positively charged particle (+q) of mass of m enters a uniform magnetic field B with a velocity v perpendicular to the field. The particle traverses a circular path. The radius of this circular path depends a) linearly on the velocity of the particle b) inversely on the velocity of the particle c) linearly on the magnetic field d) inversely on the magnetic field

14. A proton and α and particle enter a uniform magnetic field with same speed perpendicular to the magnetic field. Choose the correct alternatives: a) The radius of circular path of proton is larger b) The radius of circular path of α particle is larger c) The time period of proton is larger d) The time period of α particle is larger.

15. The magnetic field generated at a point due to a small element of a current carrying conductor depends a) linearly on the current flowing in the conduct. b) inversely on the current flowing in the conductor c) linearly on the distance r between the element and point P. d) inversely on the square of the distance r between the element and point P.

16. The magnetic field generated at a point due to a small element of a current carrying conductor depends a) linearly on the length of the element


23

b) inversely on the length of the element

c) linearly on the sine on the angle between length of the element and the line joining the element to the point P.

d) inversely on the sine of the angle between the length of the element and the line joining the element to the point P

17. The magnetic force

a) does not have the same direction as magnetic field.

b) does not have the same direction as the direction of the motion of charges

c) direction is always perpendicular to both the direction of magnetic field and the direction of the motion of charges.

d) direction is always parallel to either the direction of magnetic field or the direction of the motion of charges.

18. A charged particle moves in a gravity-free spaced without change in velocity. Which of the following are possible ?

a) The electric field and the magnetic field both are zero.

b) The electric field and the magnetic both are non-zero

c) The electric field and is zero, the magnetic field is non-zero.

d) The magnetic field is zero, the electric field is non –zero.

19. If a charged particle goes with a uniform velocity in a region containing electric magnetic field, then

a) electric field must be perpendicular to the magnetic field.

b) electric field must be parallel to the magnetic field.

c) the velocity must be perpendicular to the electric field.

d) the velocity must be perpendicular to the magnetic field.

20. Let the two current carrying wires be placed near each other in vacuum or air. The force exerted on each other

a) depends linearly on the value of current in the wires.

b) depends linearly on the length of the wires.

c) depends linearly on the distance between the wires.

d) depends inversely on the distance between the wires.

21. The magnetic field at the centre of the current carrying circular coil is

a) linearly proportional to the value of the current.

b) linearly proportional to the radius of the circular coil.

c) inversely proportional to the radius of the circular coil.

d) inversely proportional to the number of turns in the circular coil.

22. Magnetic field inside a current carrying long solenoid

a) is independent of the radius of the solenoid.

b) depends linearly on the radius of the solenoid.

c) is independent of the number of turns of the solenoid.

d) depends linearly on the number of turns of the solenoid.

23. When a charged particle moves in a uniform magnetic field at right angles to the direction of the direction of the field, which of the following quantities do not change ?

a) Path of the particle b) Speed of the particle

c) Energy of the particle d) Charge of the particle.

24. Two freely hanging long wires are connected to a battery in

a) series , then the wires repel each other b) series, then the wires attract each other

c) parallel, then the wires repel each other d) parallel, then the wires attract each other


24

25. A body is suspended from the lower end of a vertical spring. A current passes through the spring, then

a) the body shall be lifted upwards.

b) the body shall go downwards.

c) the motion of the body depends on the direction of the current in the spring.

d) the motion of the body is independent of the direction of the current in the spring.

26. A current is flowing in a circular loop of wire in clockwise direction. The magnetic field at the centre of the wire is

a) directed downward b) zero

c) inversely proportional to the radius of the loop d) directed upward.

27. An electron is moving in a liquid kept in a uniform magnetic field, in a plane perpendicular to the magnetic field. Then, the path of the electron is an inward spiral. The

a) kinetic energy of the electron decreases

b) kinetic energy of the electron increases

c) frequency of revolution of the electron remains constant.

d) frequency of revolution of the electron increases.

28. Two singly ionised isotopes of a material are accelerated through the same potential difference and enter perpendicular into a uniform magnetic field. Then,

a) the radius of the circular orbit of the heavier isotope in the magnetic field is greater than that of the lighter isotope.

b) the radius of the circular orbit of the heavier isotope in the magnetic field is less than that of the lighter isotope.

c) the kinetic energy of both the isotopes before entering the magnetic field are equal.

d) the kinetic energy of both the isotopes will remain equal in the magnetic field.

29. An electron moving in a circular orbit around the nucleus of an atom

a) exerts an electric force on the nucleus

b) does not exert an electric force on the nucleus.

c) has a magnetic dipole moment.

d) has zero magnetic dipole moment. 30. A bar of mass M, length L and carrying a current I is suspended horizontally by two wires in a

uniform magnetic field B, which is directed into the page. Then, a) the magnetic force ILB is directed downward.

b) the magnetic force ILB is directed upward.

c) the tension in each wire is (Mg+ ILB)/2.

d) the tension in each wire is (Mg– ILB)/2

31. At a certain place, the component of the earth’s magnetic field parallel to the earth’s surface is 0.35 × 10–4 T. If an electron is shot with a speed of 107 m/x vertically upward at that place, then

a) the force on the electron is 0.56 ×10–16 N

b) the acceleration on the electron is 6.1×1013 m/s2

c) the direction of force is eastward.

d) the direction of force is westward.

32. A proton is shot in the magnetic field 0.16i T with a velocity 105(i + 3j) m/x. Which of the following statements are correct ?

a) The path of the proton will be circular.

b) The path of the proton will be helical.

c) The radius of the path of the proton is 0.156 m.

d) the pitch of the path of the proton is 0.164 m.


25

33. A particle with charge q and mass m orbits perpendicular to a uniform magnetic field. The frequency of orbital motion. a) depends on the speed of the particle b) is independent of the speed of the particle c) depends linearly on q/m d) depends inversely on q/m

34. A uniformly charged disk of radius r, charge |q| and mass m with uniform mass distribution, rotates with uniform angular velocity w. Then, a) the magnitude of magnetic dipole moment is w|q| r2/2 b) the magnitude of magnetic dipole moment is w|q| r2/4 c) the magnitude of angular momentum is m r2 w/2 d) the magnitude of angular momentum is m r2 w/4

35. A current I flows through a thin wire shaped as an equilateral triangle and as a regular hexagon, which are inscribed in a circle of radius R. The magnetic induction at the centre of the

a) equilateral triangle is 033 µ I /2π R b) regular hexagon is 033 µ I /2π R.

c) equilateral triangle is 03µ I /π R d) regular hexagon is 03µ I / π R.

36. There are two rectangular wire frames A and B with same current I and same diagonal d. The angle between the diagonals for frame A is 30°, while for frame B is 60°. The magnetic induction at the centre of frame

a) A is 8 µ0 I / π 3d b) B is 8µ0 I /π 3d c) A is 8µ0 I / π d d) B is 8µ0 I /π d.

KEY : (MULTI CORRECT ANSWERS)

1) a, d 2) a, d 3) a, b 4) a, b , c 5) b, d 6) a, c, d

7) b, c 8) a, b , d 9) a, d 10) b, c 11) a, c 12) a, d

13) a, d 14) b, d 15) a, d 16) a, c 17) a, b, c 18) a, b, c

19) a, c 20) a, b, d 21) a, c 22) a, d 23) b, c, d 24) a, d

25) a, d 26) a, c 27) a, c 28) a, c, d 29) a, c 30) b, d

31) a, b, c 32) b, d 33) b, c 34) b, c 35) a, d 36) b, c

MULTIPLE CHOICE QUESTIONS : 1. If an electron travels in a uniform magnetic field normally, the path of the electron is

1) straight line 2) ellipse 3) circular 4) parabola

2. If an electron traverses uniform magnetic field obliquely, its path is

1) a spiral 2) a circle 3) an ellipse 4) a parabola

3. A magnetic needle is kept in a non uniform magnetic field. It experiences

1) force 2) torque 3) torque and force 4) none

4. Check the correct statement

1) a spinning electron must have magnetic moment

2) every gas will be affected by magnetic field

3) electrically charged particles will be affected by magnetic field when they are at rest

4) neutron will be deflected in magnetic field

5. The force experienced by charge ‘e’ moving with velocity parallel to the magnetic induction B is

1) Be V 2) BV/e 3) Be/V 4) 0

6. Two particles of masses m1 and m2 (m1 > m2) have equal charges. When they enter the magnetic field at right angles to it with same K.E, the trajectory of first particle compared to that of second particle is

1) less curved 2) more curved 3) equally curved 4) none


26

7. Positive particles coming from the space towards the earth are deflected by earth’s magnetic field towards

1) east 2) west 3) north 4) south

8. The force acting between two parallel current carrying conductors is F. If the current in each conductor and distance between them is doubled, the value of the force now is

1) F 2) 2F 3) 4F 4) 8F

9. The radius of curvature of the path of a charged particle in a uniform magnetic field is proportional to

1) charge of the particle 2) momentum of the particle 3) square root of its KE 4) both 2 and 3

10. If oo, εµ and C are the permeability of free space, permitivity of free space and velocity of light,

then 1) ooεµ = 1/C 2) ooεµ = 1/C2 3) oµ C = oε 4) ooεµ = C

11. A coil of radius π meters, 100 turns carries a current of 3A. The magnetic induction at a point on

its axis at a distance equal to 3 times its radius from its centre is

1) 7.2 x 10–6 wbm–2 2) 7.4 x 10–6 wbm–2 3) 7.5 x 10–6 wbm–2 4) 7.83 x 10–6 wbm–2 12. An α-particle of energy 2 MeV is moving in a circular path in a magnetic field. The energy

required by proton to move in the same circular path in the same magnetic field is

1) 0.5 MeV 2) 1 MeV 3) 2 MeV 4) 4 MeV

13. A vertical straight conductor carries a current vertically upwards. A point P lies in the east of it at a small distance and another point Q lies to the west of it at the same distance. The magnetic field at ‘P’ is

1) greater than at ‘Q’ 2) same as at ‘Q’

3) less than at ‘Q’ 4) depends on strength of current

14. An ammeter should have very low resistance

1) for large deflection 2) for better stability 3) so that it may not burn out 4) so that it may not change the value of current in the circuit

15. The resistance of an ideal voltmeter is 1) zero 2) 1000 Ω 3) infinity 4) 10 Ω

16. A voltmeter should have very high resistance

1) for large deflection 2) for better stability 3) so that it draws negligible current 4) so that it may not burnout

17. The moving of coil of galvanometer can be quickly stopped by

1) connecting a high resistance across the ends of the coil 2) holding a magnet near the coil 3) short circuiting the coil 4) earthing the coil

18. A volt meter has resistance of 1000 Ω. The additional resistance to be put in series to increase its range 5 times is 1) 5000 Ω 2) 200 Ω 3) 4000 Ω 4) 800 Ω

19. The sensitivity of a moving coil galvanometer depends on

1) the angle of deflection 2) earth’s magnetic field 3) torsional constant of the spring 4) moment of inertia of coil

20. Two coils one of 100 Ω and the other of 200 Ω are connected in series with a 4 V battery. A voltmeter of 200 Ω is connected in parallel with each of the coil is in turn. The voltage it shows in each case is

1) 2 C, 1 V 2) 3 V, 2 V 3) 1 V, 2 V 4) 3 V, 4 V


27

21. A galvanometer with a scale divided into 100 equal divisions has a current sensitivity of 10 division/mA and a voltage sensitivity of 1 div/mV. The shunt required to convert it into an ammeter of 5 A is 1) 5/499 Ω 2) 8/499 Ω 3) 10/499 Ω 4) 15/499 Ω

22. The deflection of a galvanometer falls to 1/10th when a resistance of 5 Ω is connected in parallel with it. If an additional resistance of 2 Ω is connected in parallel to this galvanometer, the deflection falls to 1) 1/6th 2) 1/16th 3) 2/65th 4) 3/38th

23. The end of the solenoid carrying current in clockwise direction behaves like 1) south pole 2) north pole 3) depends on strengths of current 4) none

24. Absolute unit of current is called e.m.u. because it is based on 1) heating effect of current 2) chemical effect off current 3) Piezo electric effect 4) magnetic effect of current

25. Which type of galvanometer do you use at a place containing magnetic materials to measure current 1) T.G. 2) moving coil galvanometer 3) both 4) none

26. A T.G. gives a deflection of 45° when a current of 0.1 A passes through it. The reduction factor of T.G. is 1) 10/ π 2) 2 π /10 3) 0.1 4) π /10

27. Sensitiveness of T.G. can be increased by 1) increasing ‘n’ and decreasing radius r 2) increasing ‘n’ and increasing radius r 3) decreasing ‘n’ and increasing radius 4) decreasing ‘n’ and decreasing radius r

28. For maximum accuracy in determining the current, the deflection in T.G. must be 1) 90° 2) 60° 3) 45° 4) 130°

29. Round a straight conductor carrying current, the locus of all points having the same field is a 1) straight line 2) circle 3) ellipse 4) parabola

30. The field due to a straight small conductor at a point is 4 units. At a point at twice the distance on the same line as the first, the field will be 1) 2 units 2) 4 units 3) 1 unit 4) 4/ π units

31. Two circular coils of radii 18 cm and 27 cm having same number of turns are connected in series. The ratio of magnetic induction at the centre of the coils is 1) 4 : 9 2) 9 : 4 3) 2 : 3 4) 3 : 2

32. The same T.G. is used at places A and B where the values of the horizontal components of the earth’s field are in the ratio 1 : 4. It is more sensitive at 1) A 2) B 3) both A and B 4) all places

33. Force on a conductor carrying current in a magnetic field is used in the construction of 1) T.G. 2) dynamo 3) moving coil galvanometer 4) none

34. A circular coil of one turn carries a current of 1 A. If the radius is r, it behaves as a short magnet of moment 1) π r2 2) π /r2 3) 2 π /r 4) r2/ π

35. The T.G. does not work at 1) poles 2) equator 3) at 45° latitude 4) at any latitude

36. Values of horizontal component of the earth’s field at London and at Madras are 0.18x10–4 T and 0.38x10–4 T. So the reduction factor of T.G. at Madras is 1) greater than that London 2) less than that at London 3) equal to that at London 4) we cannot say


28

37. In the above problem Tangent Galvanometer is more sensitive at 1) Madras 2) London 3) both 1 and 2 4) more

38. Two identical Tangent Galvanometers but with different turns show deflection of 60° and 30° when connected in series. The number of turns are in the ratio of

1) 3 :1 2) 3 : 1 3) 1 : 3 4) 1 : 2

39. Two T.G.s A and B have same number of turns. Their diameters are in the ratio 1:3. When they are connected in series, which shows greater deflection 1) B 2) A 3) A and B 4) None

40. A T.G. gives a deflection as 60° with a cell and a wire in series. Two more similar wires are joined in series with the first. The deflection becomes 1) 45° 2) 30° 3) 20° 4) 10°

41. The same T.G. shows different deflections at two places when the same current passes through it because 1) acceleration due to gravity is different at different places 2) horizontal component of earths field are different at different places 3) first place is at higher altitude 4) none

42. A resistance of 10 Ω is connected in series with a T.G. and the deflection is 60°. To reduce the deflection to 30° the resistance that must be connected in series with the first is 1) 10 Ω 2) 20 Ω 3) 30 Ω 4) 120 Ω

43. The deflections in a T.G. are 30° and 60° when two cells are connected one after another to it. The emf of the cells are in the ratio of

1) 1:3 2) 3:1 3) 3 :1 4) 1: 3

44. The deflection of a T.G. is 60°. The deflection is reduced to half. The resistance is increased to 1) twice the original value 2) thrice the original value 3) four times the original value 4) none

45. The sensitiveness of a moving coil galvanometer increases with 1) increasing number of turns 2) increasing number of turns and using a fine suspension wire 3) decreasing number of turns and using a fine suspension wire 4) increasing number of turns using a fine suspension wire and using a powerful magnet

46. A copper bar weighing ‘m’ rests on two rails ‘l’ apart and carrying current ‘i’ from one rail to the other. The coefficient of static friction is µ . The smallest magnetic field that would cause the bar

to slide is 1) µ mg/2 il 2) 2 µ mg/il 3) µ mg/il 4) 4 µ mg/il

47. The magnetic field is analogous to 1) potential energy 2) kinetic energy 3) both 1 and 2 4) none

48. An electron moves along a circular coil of radius 2 × 10–10 m with a uniform speed of 3x106 ms–1. The magnetic field at the centre is 1) 1.2 wb m–2 2) 1.1 wb m–2 3) 1 wb m–2 4) 0.8 wb m–2

49. Uniform magnetic field is produced by 1) earth 2) circular coil 3) bar magnet 4) solenoid

50. A wire ‘l’ in length and having a mass ‘m’ is suspended by an elastic wire in a magnetic field B. The current required to overcome the tension in suspended wire is 1) mg/3Bl 2) mg/2Bl 3) 2 mg/Bl 4) mg/Bl

51. A conducting circular loop of radius ‘r’ carries a current ‘i’. It is placed in a uniform magnetic field B0 such that B0 is perpendicular to the plane of the loop. The magnetic force acting on the loop is 1) B0 ir 2) 2 π irB0 3) zero 4) B0 π ir


29

52. A circular coil of wire carries a current. PQ is a part of a long wire carrying current and passing close to circular coil, if the directions of the current are shown, the direction of the force on PQ is 1) normal to the plane of the circle 2) parallel to PQ, towards P 3) at right angles to PQ, to the left 4) parallel to PQ, towards Q

53. Two wires of lengths in the ratio 2:3 are wound into circular coils having turns in the ratio 1:2. They are connected in series in a circuit carrying current. Then the ratio of magnetic induction at their centres is 1) 1:3 2) 4:3 3) 3:4 4) 3:8

54. Three wire A, B and C carrying currents. The currents are flowing perpendicular to the plane of the paper as shown. The current through A is 5 amperes. The currents through B and C are 2 amperes and 2 amperes. The separation between A and B is 10 cm. What is the separation between B and C so that the wire C is at rest. Assume A and B are fixed 1) 5 cm 2) 6.67 cm 3) 3.33 cm 4) 10 cm

55. In the diagram if volt meters shows 5 volts and ammeter A shows 1 ampere, then the value of Resistance R is 1) greater than 5 Ω 2) less than 5 Ω 3) equal to 5 Ω 4) can not say

56. A proton, a deuteron and an alpha particle are accelerated through the same potential difference from rest. Then they are allowed to pass normal to the direction of the magnetic field, then their radii of curvature of their paths is

1) 1 : 1: 1 2) 1 : 2 : 1 3) 1: 2 : 2 4) 2 : 2 : 1

57. In the circuit if Voltsmeter V shows 5 volts and Ammeter A shows 1 ampere then, the value R is 1) greater than 5 Ω 2) less than 5 Ω 3) equal to 5 Ω 4) none

58. A circular coil carrying current be have as a magnetic shell of moment M. If the same coil is rewound so that the number of turns is doubled, the magnetic moment is 1) M/2 2) M 3) M/4 4) 2M

59. A current carrying conductor in the form of a circular coil produces a magnetic field when connected across a cell of negligible internal resistance. The conductor is then stretched to 4 times, its length by passing it through a die and then connected across the same cell again in the form of circular coil but having radius half that in the previous case. Then the ratio magnetic induction in 1st case and second case is at their centres is 1) 1 : 4 2) 1 : 1 3) 1 : 16 4) 16 : 1

60. Two copper wires of lengths in the ratio 1:2 have thicknesses in the ratio 3:4. They are wound in the form of circular coils having turns in the ratio 2:3. If they are connected in parallel what is the ratio of magnetic flux densities at their centres? 1) 1 : 1 2) 1 : 2 3) 4 : 9 4) 1 : 4

61. Two parallel conductors A and B are carrying current of 10 A and 5 A. They are separated by a distance 5 cm. Then the distance zero induction point from B is 1) 5 cm towards A 2) 5 cm away from A 3) 10 cm towards A 4) 10 cm away from A

62. A horizontal rod of length l and m is placed an a smooth inclined plane of angle θ so that the length of the rod is parallel to the edge. A magnetic field and induction B is applied vertically and the current passing through the rod is so that the rod remains stationary is (Assume all are in S.I. units)

1) θtanBlmg

2)Blmg

3) θcotBlmg

4) θeccosBlmg

P

Q

A B Cx o o

10 cm d

V

A R

V

A R


30

63. The radius of curvature of the path of charged particle in a uniform magnetic field is directly proportional to 1) the charge on the particle 2) the momentum of the particle 3) the energy of the particle 4) the intensity of the field

64. A beam of charged particles is passed through a magnetic field. The work done on the beam by the field is 1) zero 2) independent on the speed of the beam

3) dependent on the deflection of the beam 4) dependent on the magnetic induction B

65. When a charged particle enters a uniform magnetic field, its kinetic energy

1) increases 2) decreases 3) remains constant 4) becomes zero

66. The time rate of the work done by a magnetic field B

on a charged particle q moving in a helical path is 1) qB 2) qB/V 3) qB2 4) zero

67. A proton and an alpha particle enter in a uniform magnetic field with the same velocity. The period of rotation of alpha particle will be 1) four times that of proton 2) two times that of proton 3) three times that of proton 4) same as that of proton

68. The direction of the magnetic field produced by a linear current is given by 1) right hand thumb rule 2) Fleming’s left hand rule 3) Joule’s law 4) Ampere’s law

69. The field inside a solenoid is 1) directly proportional to its length 2) directly proportional to the current 3) inversely proportional to the number of turns 4) inversely proportional to the current

70. Two long wires are hanging freely. They are joined first in parallel and then is series and then are connected to a battery. In both the cases, which type of force acts between the two wires ? 1) attraction force when in parallel and repulsion force when in series 2) repulsion force when in parallel and attraction force when in series 3) repulsion force in both cases 4) attraction force in both the cases

71. The sensitivity of a moving coil galvanometer depends on 1) the angle of deflection 2) earth’s magnetic field 3) torsional constant of the spring 4) the moment of inertia of the coil

72. The sensitivity of a tangent galvanometer will increases when 1) the number of turns in the coil is decreased 2) the number of turns in the coil is increased 3) the radius of the coil is increased 4) it is independent of the radius of the coil

73. A voltmeter always gives a less value of the actual potential difference because 1) some energy is lost in moving the needle 2) internal resistance of a cell plays its role 3) it absorbs some energy 4) both 1 and 2

74. Which of the following is likely to have the largest resistance ? 1) moving coil galvanometer 2) ammeter of range 1 A 3) voltmeter of range 10 V 4) a copper wire of length 1 m and diameter 3mm

75. A voltmeter has a resistance of G ohm and range V volt. The value of the resistance used in series to convert it into a voltmeter of range nV volt is 1) nG 2) (n–1)G 3) G/n 4) G/(n–1)

76. An ammeter has a resistance of G ohm and range of i ampere. The value of the resistance used in parallel to convert it into an ammeter of range ni ampere is 1) nG 2) (n–1)G 3) G/n 4) G/(n–1)


31

77. A circular coil carrying current behaves as a 1) bar magnet 2) horse shoe magnet 3) magnetic shell 4) solenoid

78. A straight conductor is placed along the axis of a circular coil perpendicular to the plane of the coil. Then electric current is passed through both 1) only straight conductor experiences force 2) only coil experiences force 3) both experience force 4) none experience force

79. Pick up the correct statement 1) ammeter is connected in series in a circuit because its resistance is generally high 2) voltmeter is connected in parallel because its resistance is generally low 3) voltmeter is connected in parallel because its resistance is generally high 4) ammeter is connected in parallel because its resistance is generally low

80. A spring is held vertically downward and then a current I is passed through it. Now the length of the spring 1) increases 2) decreases 3) does not change 4) oscillates

81. The magnetic field between he magnetic poles of the magnet in a moving coil galvanometer is 1) cylindrical 2) circular 3) radial 4) concave

82. A vertical wire carries a current in upward direction. An electron beam sent horizontally towards the wire will be deflected 1) towards right 2) towards left 3) upwards 4) downwards

83. A current carrying, straight wire is kept along the axis of a circular loop carrying a current. The straight wire 1) will exert an inward force on the circular loop 2) will exert an outward force on the circular loop 3) will not exert any force on the circular loop 4) will exert a force on the circular loop parallel to itself

84. A proton beam is going from north to south and an electron beam is going from south to north. Neglecting the earth’s magnetic field, the electron beam will be deflected 1) towards the proton beam 2) away from the proton beam 3) upwards 4) downwards

85. A circular loop is kept in that vertical plane which contains the north-south direction. It carries a current that is towards north at the topmost point. Let A be a point on the axis of the circle to the east of it and B a point on this axis to the west of it. The magnetic field due to the loop 1) is towards east at A and towards west at B 2) is towards west at A and towards east at B 3) is towards east at both A and B 4) is towards west at both A and B

86. Consider the situation shown in figure. The straight wire is fixed but the loop can move under magnetic force. The loop will 1) remain stationary 2) move towards the wire 3) move away from the wire 4) rotate about the wire

87. A charged particle is moved along a magnetic field line. The magnetic force on the particle is 1) along its velocity 2) opposite to its velocity 3) perpendicular to its velocity 4) zero

88. A moving charge produces 1) electric field only 2) magnetic field only 3) both of them 4) none of them

89. A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to 1) the velocity 2) the momentum 3) the kinetic energy 4) none of these

i1 i2


32

90. Two particles X and Y having equal charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii R1 and R2 respectively. The ratio of the mass of X to that of Y is 1) (R1/R2)

1/2 2) R1/R2 3) (R1/R2)2 4) R1R2

91. Two parallel wires carry currents of 20 A and 40 A in opposite directions. Another wire carrying a current antiparallel to 20 A is placed midway between the two wires. The magnetic force on it will be 1) towards 20 A 2) towards 40 A 3) zero 4) perpendicular to the plane of the currents

92. Two parallel, long wires carry currents i1 and i2 with i1>i2. When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 µ T. If the direction of i2 is reversed, the field becomes 30 µ T. The ratio i1/i2 is

1) 4 2) 3 3) 2 4) 1 93. Consider a long, straight wire of cross-sectional area A carrying a current i. Let there be n free

electrons per unit volume. An observer places himself on a trolley moving in the direction

opposite to the current with a speed v=nAe

i and separated from the wire by a distance r. The

magnetic field seen by the observer is very nearly

1) r2

io

πµ

2) zero 3) r

io

πµ

4) r

i2 o

πµ

94. A long, straight wire carries a current along the Z-axis. One can find two points in the X-Y plane such that 1) the magnetic fields are equal 2) the directions of the magnetic fields are the same 3) the magnitudes of the magnetic fields are equal 4) the field at one point is opposite to that at the other point

95. A long, straight wire of radius R carries a current distributed uniformly over its cross-section. The magnitude of the magnetic field is 1) maximum at the axis of the wire 2) minimum at the axis of the wire 3) maximum at the surface of the wire 4) minimum at the surface of the wire

96. A hollow tube is carrying an electric current along its length distributed uniform over its surface. The magnetic field 1) increases linearly from the axis to the surface 2) is constant inside the tube 3) is zero at the axis 4) is zero just outside the tube

97. In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero 1) outside the cable 2) inside the inner conductor 3) inside the outer conductor 4) in between the two conductors

98. A steady electric current is flowing through a cylindrical conductor 1) the electric field at the axis of the conductor is zero 2) the magnetic field at the axis of the conductor is zero 3) the electric field in the vicinity of the conductor is zero 4) the magnetic field in the vicinity of the conductor is zero

99. The magnetic effect of electric current was discovered by 1) Fleming 2) Faraday 3) Ampere 4) Oersted

100. A proton moving with a constant velocity passes through a region of space without any change in the velocity. If E and B represent the electric and magnetic fields respectively, this region of space may have 1) E=0, B=0 2) E=0, B ≠ 0 3) E ≠ 0, B=0 4) E ≠ 0, B ≠ 0


33

101. An electron is injected into a region of uniform magnetic flux density, with components of velocity parallel to and normal to the flux. The path of the electrons is

1) a helix 2) straight line 3) parabola 4) ellipse

102. An electron having a charge e moves with a velocity v in X-direction. An electric field acts on it in Y-direction. The force on the electron acts in the

1) positive direction of Y-axis 2) negative direction of Y-axis 3) positive direction of Z-axis 4) negative direction of Z-axis

103. An electron moving with a speed u along the positive x-axis at y = 0 enters a region of uniform magnetic field kBB 0−= which exits to the right of y-axis the electron exits from the region after

some time with the speed v at ordinate y. Then 1) v > u, y < 0 2) v = u, y > 0 3) v > u, y > 0 4) v = u, y < 0

104. The energy in a current carrying coil is stored in the form of

1) electric field 2) magnetic field 3) dielectric strength 4) heat

105. Magnetic field is not associated with

1) a charge in uniform motion 2) an accelerated charge

3) a decelerated charge 4) a stationary charge

106. There is a magnetic field acting in a plane perpendicular to this sheet of paper downwards into the paper. Particles in vacuum move in the plane of the paper from left to right. The path indicated could be travelled by a

1) cation 2) neutron

3) proton 4) electron

107. The time rate of the work done by a magnetic field B on a charged particle q moving in a helical path is

1) qB 2) aB/v 3) qB2 4) zero

108. A current is passed through a straight wire. The magnetic field established around it has its lines of forces

1) circular and endless 2) oval in shape and endless

3) straight 4) radially outward

109. If a copper rod carries a direct current, the magnetic field associated with the current will be

1) only inside the rod 2) only outside the rod

3) both inside and outside the rod 4) neither inside nor outside the rod

110. If a long hollow copper pipe carries a direct current, the magnetic field associated with the current will be

1) only inside the pipe 2) only outside the pipe

3) neither inside nor outside the pipe 4) both inside and outside the pipe

111. A live cable is hidden in a wall. Its position can be located with the help of a

1) wattmeter 2) moving coil galvanometer

3) magnetic needle 4) hot wire ammeter

112. A current i flows along infinitely long straight thin conductor. Then the magnetic induction at an point on the conductor is

1) ∞ 2) zero 3) ri2

.4

0

πµ

4) ri2

113. A current i ampere flows along an infinitely long straight thin walled tube. Then the magnetic induction at any point inside the tube is

1) ∞ 2) zero 3) ri2

.4

0

πµ

4) ri2

x

x x

xx x x


34

114. An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of i ampere and the radius of the circular loop is r metre. Then the magnetic induction at the centre of the circular art is

1) zero 2) infinite 3) ri2

.4

0

πµ

( )1+π tesla 4) ri2

.4

0

πµ

( )1−π tesla

115. In the given figure, the straight parts of the wire very long. The magnetic induction at O is

1)r2

i

r4

i 00

πµ

+µ

out of the page 2) r4

i

r2

i 00

πµ

+µ

out of the page

3) r4

i

r4

i 00

πµ

+µ

into the page 4) r2

i

r4

i 00

πµ

+µ

into the page

116. The variation of magnetic field B due to a long straight current-carrying wire with distance r from the wire is given by 1) 2) 3) 4)

117. A current i ampere flows in the loop having a circular arc of radius r metre subtending an angle θ as shown in the figure. The magnetic field at the centre of 0 the circle is

1) r4

i0

πθµ

2) 2

0

r4

sini

π

θµ

3) r2

sini2 0 θµ 4)

r2

sini0 θµ

118. In the figure, there are two semi-circles of radii r1 and r2 in which a current i is flowing. The magnetic induction at the centre O will be

1) )rr(4

i21

0 +µ

2) )rr(4

i21

0 −µ

3) ⎟⎟⎠

⎞⎜⎜⎝

⎛ +µ

21

210

rr

rr

4

i 4) ⎟⎟

⎠

⎞⎜⎜⎝

⎛ −µ

21

210

rr

rr

4

i

119. A straight conductor carrying a direct current i ampere is split into circular loop as shown in the figure. The magnetic induction at the centre of the circular loop of radius R metre is

1) zero 2) R

i2.

4

i0 ππ

µtesla

3) Ri2

.4

0

πµ

tesla 4) R4

i0µtesla

120. A battery of e.m.f ε volt is connected across a coil of uniform wire as shown. The radius of the coils is ‘a’ metres and the total resistance of the wire is R ohm. The magnetic field at the centre of O of the coil is

1) zero 2) Ra20εµ

3) Ra

0εµ 4)

Ra

2 0εµ

121. A long thin wire is bent as shown in the figure. The radius of the semicircular part is r meters. If a current of i ampere flows through the wire, then the magnetic induction at O in tesla is

1) )1

1(r4i0

π+µ

out of the page 2) )1

1(r

i0

π+

µ into the page

3) )21

1(r2

i0

π+

µout of the page 4) )

21

1(r2

i0

π+

µ into the page

i

i

or

r1

r2

o

i

o90o

B

r

B

r

B

r

B

r

o r

θi


35

122. In a moving coil galvanometer, we use a radial magnetic field so that the galvanometer scale is

1) logarithmic 2) exponential 3) linear 4) nonlinear

123. The current that must flow through the coil of a galvanometer so as to produce a deflection of one division on its scale is called

1) charge sensitivity of the galvanometer 2) current sensitivity of the galvanometer

3) micro-volt sensitivity 4) reduction factor of galvanometer

124. The sensitivity of a tangent galvanometer will increase when

1) the number of turns in the coil is decreased 2) the number of turns in the coil is increased

3) the radius of the coil is increased 4) it is independent of the radius of the coil

125. A voltmeter always gives a less value of the actual potential difference because

1) some energy is lost in moving the needle 2) internal resistance of a cell plays its role

3) it absorbs some energy 4) both (1) and (2) are true

126. The resistance of an ideal ammeter should be

1) zero 2) moderate 3) very high 4) infinitey

127. If magnetic field at O is equal to zero the value of θ is

1) π – 2 2) 2π – 2 3) 2π 4) π/2

128. Two coils in two moving coil galvanometers have there are as in the ratio of 2 : 3 and number of turns in the ratio 4 : 5. These two coils carry the same current and are situated in the same field. The defections produced by these two coils will be in the ratio of

1) 8 : 15 2) 15 : 8 3) 15 :4 4) 15:22

129. A conducting rod of length l and mass m is moving down a smooth inclined plane of inclination θ with constant velocity v. A current i is flowing in the conductor in a direction perpendicular to

paper inwards. A vertically upward magnetic field B

exists in space.

Then magnitude of magnetic field B

is

1) θsinil

mg 2) θtan

ilmg

3)ilcosmg θ

4)θsinil

mg

130. Magnetic field at the centre of a circular loop of area A is B. Then magnetic moment of the loop will be

1) πµ0

2BA 2) A

BA

0µ 3)

0

ABAµ

4) πµABA2

0

131. A uniform magnetic field B

= jB0 exists in space. A particle of mass m and charge q is projected

towards negative x-axis with speed v from a point (d, 0, 0). The maximum value of v for which the particle does not hit the y-z plane is

1) dmBq2

2) m

Bqd 3)

dm2Bq

4) m2

Bqd

132. A nonconducting disc of radius R is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity ω. Charge q is uniformly distributed over its surface. The magnetic moment of the disc is

1) 2Rq41 ω 2) Rq

21 ω 3) Rqω 4) 2Rq

21 ω

υ

θ Side View

B

θ O


36

133. A conducting rod of mass m and length l is placed over a smooth horizontal surface. A uniform magnetic field B is acting perpendicular to the rod. Charge q is suddenly passing through the rod and it acquires an initial velocity v on the surface, then q is equal to

1) Blmv2

2) mv2Bl

3)Blmv

4) m2

Blv

134. A wire of length l is bent in the form of a circular coil of some turns. A current i flows through the coil. The coil is placed in a uniform magnetic field B. The maximum torque on the coil can be

1) π4

iBl2 2)

π

2iBl 3)

π2iBl2

4) π

2iBl2

135. Dimensions of magnetic flux are 1) MLT–3A2 2) ML2T–2A–1 3) ML–2T2A 4) ML–2TA–1

136. The magnetic field at the centre of an equilateral triangular loop of side 2L and carrying a current is

1) L4

i9 0

πµ

2) L4

i33 0

πµ

3) L

i32 0

πµ

4) L4

i3 0

πµ

137. Ratio of magnetic field at the centre of a current carrying coil of radius R and at a distance of 3R on its axis is

1) 1010 2) 1020 3) 102 4) 10

138. Magnetic moment of an electron in nth orbit of hydrogen atom is

1) m

nehπ

2) m4

nehπ

3) m2

mehπ

4) m4

mehπ

139. The ratio of magnetic field at the centre of a current carrying circular coil to its magnetic moment is x. if the current and radius both are doubled the new ratio will become 1) 2x 2) 4x 3) x/4 4) x/8

140. Magnetic field at the centre of a circular coil of radius R and carrying a current i is

a) R2

i0µ b)

Rc2

i

02ε

c) R2

i0

πµ

d) R2

ic

0

2

ε

(c = speed of light) 1) a and b are correct 2) b and c are correct 3) c and d are correct 4) ‘a’ only correct

141. A charged particle is projected in a plane perpendicular to uniform magnetic field. The areal velocity (area swept per unit time) of the particle is a) directly proportional to kinetic energy of particle b) directly proportional to momentum of the particle c) inversely proportional to magnetic field strength d) inversely proportional to charge on particle 1) a, c and d are correct 2) a, b and c are correct 3) ‘a’ only correct 4) All are correct

142. H+, He+ and O+2 all having the same kinetic energy pass through a region in which there is a uniform magnetic field perpendicular to their velocity. The masses of H+, He+ and O+2 are 1 amu, 4 amu and 16 amu respectively. Then a) H+ will be deflected most b) O+2 will be deflected most c) He+ and O+2 will be deflected equally d) all will be deflected equally 1) a and b are correct 2) b and c are correct 3) a and c are correct 4) ‘c’ only correct

143. A wire of length ‘ ’ carries a current i0 along x-axis. A magnetic field exists which is given by

B

= B0( kji ++ )T. The magnitude of magnetic force acting on the wire is

1) 00iB 2) 2 00iB 3) 3 00iB 4) zero


37

144. Protons having kinetic energy E emerge from an accelerator as a narrow beam. The beam is bent misses a plane target kept at a distance in front of the accelerator. The magnetic field is (m → mass of a proton, q → change of proton).

1)qmE2

2) qmE22

3) qmE24

4) q2

mE2

145. A particle having mass m and charge q is released from rest at the origin in a region in which

electric field and magnetic field are given by jBB o−=

and kEE 0=

. If s is the distance travelled,

then the speed of the particle is

1)m

sqE0 2) m

sqE2 0 3)m2

sqE0 4) m

sqB2 0

146. A solid sphere of radius r and mass m which has a charge q distributed uniformly over its volume. The sphere is rotated about a diameter with an angular speed w. If ‘µ’ is magnetic moment and ‘L’ is angular momentum, then µ/L = 1) q/m 2) q/4m 3) q/2m 4) m/2q

147. If n is the number of moving charges(q) per unit volume and vd is the drift velocity then current density is

1) dv

nq 2) nqvd 3) 2nqvd 4)

2nqvd

148. The figures of merit of two galvanometers with resistance of 100 Ω and 50Ω are respectively 10–8 amp per division and 2 × 10–5 amp per division respectively. The voltage sensitivity is (div/volt) 1) more for first 2) more for second 3) equal for both 4) data is incomplete

149. A deuteron of kinetic energy 50 keV is describing a circular orbit of radius 0.5 m in a plane perpendicular to magnetic field B. The kinetic energy of the proton that describes a circular orbit of radius 0.5 m in the same plane with the same B. 1) 25 keV 2) 50 keV 3) 200 keV 4) 100 keV

150. A particle of charge ‘q’ and mass ‘m’ enters in the uniform magnetic field ‘B’ at an angle θ with velocity v. The forward distance covered during one complete rotation is

1) qBcosv2 θπ

2) qB

sinmv2 θπ 3)

qBxmcosv θ

4)qB

cosmv2 θπ

151. An electron move with a constant speed v along a circle of radius r. The magnetic moment of the circulating election is

1) r2

evπ

2)2

evr 3)

e2mvr

4) zero

152. Which of the following particles will describe the smallest circle where projected with the same velocity perpendicular to a magnetic field ? 1) electron 2) proton 3) He+ 4) Li+

153. Which of the following particles will have minimum frequency of revolution when projected with the same velocity perpendicular to a magnetic field ? 1) electron 2) proton 3) He+ 4) Li+

154. A charged particle is projected in a plane parallel to a uniform magnetic field. The area a bounded by the path described by the particle is proportional to 1) the velocity 2) the momentum 3) the kinetic energy 4) none of these

155. Which of the following graph represents best the variation of magnetic field along the axis of circular coil. 1) 2) 3) 4)

x→

B

x→ B ↑

x →

B ↑

x →

↑ B


38

156. A current of 15 A is directed along the positive x-axis and perpendicular to a magnetic field. The conductor experiences a magnetic force per unit length of 0.12 Nm–1 in the negative y-direction. The magnitude and direction of the magnetic field in the region through which the current passes is 1) 8 × 10–3 T in the –z direction 2) 4 × 10–3 T in the +y direction 3) 4 × 10–3 in the –x direction 4) 8 × 10–3 T in the + z direction

157. Two long straight conductors carry currents of 5 A each. They are separated by a distance of 10 cm. The points P1 and P2 are at 10 cm and 20 cm respectively. Then the magnetic induction fields. a) at the point O, midway between the wires is zero b) at the point P1, 0.5×10–5 T out of the page c) at the point O, midway between the wires is 4 × 10–5 T, into the page d) at the point P2, zero 1) a and b are true 2) b and c are true 3) c and d are true 4) b and d are true

158. A rectangular current loop is located near a long straight wire that carriers a current of 12A. The current in the loop is 25A.The net force acting on the loop is 1) 2.4 × 10–4N, attractive 2) 1.8 × 10–4N, attractive 3) 2.4 × 10–4N, repulsive 4) 1.2 × 10–4N, repulsive

159. An electrical meter of internal resistance 20 Ω gives a full scale deflection when 1 mA current flows through it. The maximum current, that can be measured by using three resistors of resistance 12 Ω each, in mA is 1) 10 2) 8 3) 6 4) 4

KEY :

1) 3 2) 1 3) 3 4) 1 5) 4 6) 1 7) 1 8) 2 9) 4 10) 2

11) 3 12) 3 13) 2 14) 4 15) 3 16) 3 17) 3 18) 3 19) 3 20) 3

21) 3 22) 3 23) 1 24) 4 25) 2 26) 3 27) 1 28) 3 29) 2 30) 3

31) 4 32) 1 33) 3 34) 1 35) 1 36) 1 37) 2 38) 2 39) 2 40) 2

41) 2 42) 2 43) 1 44) 2 45) 4 46) 3 47) 2 48) 1 49) 4 50) 4

51) 3 52) 3 53) 4 54) 2 55) 2 56) 3 57) 1 58) 1 59) 2 60) 1

61) 2 62) 1 63) 2 64) 1 65) 3 66) 4 67) 2 68) 1 69) 2 70) 1

71) 3 72) 2 73) 2 74) 3 75) 2 76) 4 77) 3 78) 4 79) 3 80) 2

81) 3 82) 3 83) 3 84) 1 85) 4 86) 2 87) 4 88) 3 89) 3 90) 3

91) 2 92) 3 93) 1 94) 2,3,4 95) 2,3 96) 2,3 97) 1 98) 2,3 99) 4 100) 1,2,4

101) 1 102) 2 103) 4 104) 2 105) 4 106) 4 107) 4 108) 1 109) 3 110) 2

111) 3 112) 2 113) 2 114) 4 115) 1 116) 1 117) 1 118) 3 119) 1 120) 1

121) 1 122) 3 123) 2 124) 2 125) 2 126) 1 127) 2 128) 1 129) 2 130) 4

131) 2 132) 1 133) 3 134) 1 135) 3 136) 1 137) 1 138) 2 139) 4 140) 1

141) 1 142) 3 143) 2 144) 1 145) 2 146) 3 147) 2 148) 1 149) 4 150) 4

151) 2 152) 1 153) 4 154) 3 155) 3 156) 4 157) 2 158) 2 159) 3

0.5 m 25 A

0.15 m 0.1 m

12A

5 A 5 A

O

10 cm

10 cm 20 cm

P2 P1

electromagnetism 1

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