TO THE TO THE EXITING EXITING WORLDWORLD

OF OF

PHYSICSPHYSICSCLASS XIICLASS XII

B.SESHA SAI

PGT PhysicsKV NO1.BHUBANESWAR

DEVELOPED BYDEVELOPED BY

B.SESHA SAIB.SESHA SAIPGT PHYSICSPGT PHYSICS

KENDRIYA VIDYALAYA NO1,BHUBANESWARKENDRIYA VIDYALAYA NO1,BHUBANESWAR

ELECTROSTATICSELECTROSTATICS THE BRANCH OF PHYSICS DEALING WITH THE BRANCH OF PHYSICS DEALING WITH

CHARGES AT REST AND THEIR PROPERTIESCHARGES AT REST AND THEIR PROPERTIES STATIC ELECTRICITY WAS FIRST OBSERVED BY STATIC ELECTRICITY WAS FIRST OBSERVED BY

THALES OF MILETUS IN 600 BC WHEN HE FOUND THALES OF MILETUS IN 600 BC WHEN HE FOUND THAT AMBER WHEN RUBBED WITH FUR THAT AMBER WHEN RUBBED WITH FUR ACQUIRED THE PROPERTY OF ATTRCACTING ACQUIRED THE PROPERTY OF ATTRCACTING TINY PIECES OF SAW DUST ETC.TINY PIECES OF SAW DUST ETC.

ELECTRICITY PRODUCED BY RUBBING IS CALLED ELECTRICITY PRODUCED BY RUBBING IS CALLED FRICTIONAL ELECTRICITYFRICTIONAL ELECTRICITY

SINCE THE CHARGES SO PRODUCED ARE AT REST SINCE THE CHARGES SO PRODUCED ARE AT REST IT IS ALSO CALLED STATIC ELECTRICITYIT IS ALSO CALLED STATIC ELECTRICITY

CHARGES ARE PRODUCED BY TRANSFER OF CHARGES ARE PRODUCED BY TRANSFER OF ELECTRONSELECTRONS

IN 1600 AD, DR. WILLIAM GILBERT, COURT PHYSICIAN TO QUEEN ELIZABETH I OF ENGLAND, PUBLISHED THE BOOK (DE MAGNETO) IN WHICH HE MADE AN ACCOUNT OF ALL THE EXPERIMENTS AND OBSERVATIONS MADE SO FAR IN THE FIELD OF ELECTROSTATICS.GILBERT FOUND THAT THERE ARE TWO KINDS OF CHARGES AND THAT LIKE CHARGES REPEL AND UNLIKE CHARGES ATTRACT.HE NAMED THE TWO KINDS OF CHARGES AS RESINOUS AND VITREOUS.THE CHARGE ACQUIRED BY AMBER OR EBONITE (WHEN RUBBED WITH WOOL OR FUR) WAS CALLED RESINOUS AND THE OTHER KIND OF CHARGE WAS CALLED VITREOUS.

BENJAMIN BENJAMIN FRANKLINFRANKLIN, , AN AMERICAN AN AMERICAN SCIENTISTSCIENTIST

Introduced the convention Introduced the convention according to which resinous charge according to which resinous charge was called negative and the other was called negative and the other was called positivewas called positive

CONSERVATION OF CHARGESCONSERVATION OF CHARGES

THE TOTAL CHARGE IN ANY SYSTEM IS THE TOTAL CHARGE IN ANY SYSTEM IS ALWAYS CONSERVEDALWAYS CONSERVED

NET CHARGE CAN NEITHER BE CREATED NET CHARGE CAN NEITHER BE CREATED NOR BE DESTROYED IN ISOLATIONNOR BE DESTROYED IN ISOLATION

CHARGES CAN ONLY BE PRODUCED OR CHARGES CAN ONLY BE PRODUCED OR DESTROYED IN EQUAL AND OPPOSITE PAIRSDESTROYED IN EQUAL AND OPPOSITE PAIRS

THE TOTAL CHARGE BEFORE AND AFTER THE TOTAL CHARGE BEFORE AND AFTER ANY REACTION REMAINS THE SAME.ANY REACTION REMAINS THE SAME.

QUANTIZATION OF CHARGEQUANTIZATION OF CHARGE

THE CHARGE PRESENT IN ANY BODY IS THE CHARGE PRESENT IN ANY BODY IS ALWAYS THE INTEGRAL MULTIPLE OF ALWAYS THE INTEGRAL MULTIPLE OF FUNDAMENTAL CHARGE FUNDAMENTAL CHARGE THE THE CHARGE OF AN ELECTRON (CHARGE OF AN ELECTRON (1.6 X 101.6 X 10-19-19CC))

NO BODY CAN POSSESS FRACTIONAL NO BODY CAN POSSESS FRACTIONAL ELECTRONIC CHARGE (IN THE ELECTRONIC CHARGE (IN THE MACROSCOPIC WORLD)MACROSCOPIC WORLD)

QUARKSQUARKS ARE PARTICLES CONSIDERED TO POSSESS ARE PARTICLES CONSIDERED TO POSSESS

FRACTIONAL ELECTRONIC CHARGES -- FRACTIONAL ELECTRONIC CHARGES -- ± 1/3 ± 1/3 e, ± 2/3 e …..e, ± 2/3 e …..

THERE ARE SIX TYPES OF QUARKSTHERE ARE SIX TYPES OF QUARKS UP, UP, DOWN, TOP, BOTTOM, CHARM AND DOWN, TOP, BOTTOM, CHARM AND STRANGESTRANGE

BUT THE EXISTENCE OF QUARKS DONOT BUT THE EXISTENCE OF QUARKS DONOT VIOLATE THE LAW OF CONSERVATION OF VIOLATE THE LAW OF CONSERVATION OF CHARGE. IT ONLY CHANGES THE CHARGE. IT ONLY CHANGES THE MAGNITUDE OF FUNDAMENTAL CHARGE MAGNITUDE OF FUNDAMENTAL CHARGE TO THAT OF THE LOWEST POSSIBLE TO THAT OF THE LOWEST POSSIBLE CHARGE ON QUARKS.CHARGE ON QUARKS.

ALSO, QUARKS CANNOT EXIST FREELY. ALSO, QUARKS CANNOT EXIST FREELY. THEY ARE ALWAYS FOUND COMBINED TO THEY ARE ALWAYS FOUND COMBINED TO FORM INTEGRAL MULTIPLES OF FORM INTEGRAL MULTIPLES OF ELECTRONIC CHARGE.ELECTRONIC CHARGE.

QuarkQuark SymbolSymbol SpinSpin ChargeChargeBaryonBaryon

NumNumberber

SS CC BB TTMass*Mass*

UpUp UU 1/21/2 +2/3+2/3 1/31/3 00 00 00 00 360 MeV360 MeV

DownDown DD 1/21/2 -1/3-1/3 1/31/3 00 00 00 00 360 MeV360 MeV

CharmCharm CC 1/21/2 +2/3+2/3 1/31/3 00 +1+1 00 00 1500 MeV1500 MeV

StrangeStrange SS 1/21/2 -1/3-1/3 1/31/3 -1-1 00 00 00 540 MeV540 MeV

TopTop TT 1/21/2 +2/3+2/3 1/31/3 00 00 00 +1+1 174 GeV174 GeV

Bottom Bottom BB 1/21/2 -1/3-1/3 1/31/3 00 00 +1+1 00 5 GeV5 GeV

COULOMB’S LAWCOULOMB’S LAW

THE FORCE OF ATTRACTION OR REPULSION THE FORCE OF ATTRACTION OR REPULSION BETWEEN TWO POINT CHARGES IS DIRECTLY BETWEEN TWO POINT CHARGES IS DIRECTLY PROPORTIONAL TO THE PRODUCT OF THE PROPORTIONAL TO THE PRODUCT OF THE AMGNITUDE OF THE CHARGES AND AMGNITUDE OF THE CHARGES AND INVERSELY PROPORTIONAL TO THE SQUARE INVERSELY PROPORTIONAL TO THE SQUARE OF THE DISTANCE BETWEEN THEM.OF THE DISTANCE BETWEEN THEM.

MATHEMATICALLYMATHEMATICALLY

221

04

1

r

QQF

RELATIVE PERMITIVITYRELATIVE PERMITIVITY

Is defined as the ratio of the force between two Is defined as the ratio of the force between two point charges separated in vacuum to the force point charges separated in vacuum to the force between the same two charges separated by between the same two charges separated by the same distance while kept in the medium.the same distance while kept in the medium.

i.e. i.e. rr= F= F00 /F /Fmm

PRINCIPLE OF SUPER POSITIONPRINCIPLE OF SUPER POSITION

States that when there are a number of point States that when there are a number of point charges, the net force on any one of the charges, the net force on any one of the charges is equal to the vector sum of the forces charges is equal to the vector sum of the forces due to the individual charges.due to the individual charges.

i.e. i.e.

FF11 = F = F1212+ F+ F1313+ F+ F14 14 + ……+ ……

DEFINE 1 COULOMBDEFINE 1 COULOMB

One coulomb is defined as that charge which One coulomb is defined as that charge which when kept one metre apart from an equal and when kept one metre apart from an equal and similar charge in vacuum, repels it with a force similar charge in vacuum, repels it with a force of 9 x 10of 9 x 1099N.N.

ELECTRIC FIELDELECTRIC FIELD QualitativelyQualitatively

The region of space around a charge where it can The region of space around a charge where it can exert a force of electrical origin on another charge.exert a force of electrical origin on another charge.

QuantitativelyQuantitatively The intensity of ELECTRIC FIELD at any point is The intensity of ELECTRIC FIELD at any point is

defined as the force exerted per unit charge by a defined as the force exerted per unit charge by a positive test charge kept at that point.positive test charge kept at that point.

0

0lim

q

FE

oq

ELECTRIC LINES OF FORCEELECTRIC LINES OF FORCE

Are imaginary lines of force such that the Are imaginary lines of force such that the tangent to it at any point gives the direction of tangent to it at any point gives the direction of electric field at that point.electric field at that point.

A positive point charge free to move will A positive point charge free to move will move in the direction of electric field and a move in the direction of electric field and a negative point charge will move in a direction negative point charge will move in a direction opposite to the direction of electric field along opposite to the direction of electric field along an electric line of force.an electric line of force.

The lines of force to represent uniform electric field are as shown below

The electric lines of force due to point charge q < 0 are as shown below

The electric lines of force due to point charge q > 0 are as shown below

PROPERTIES OF ELECTRIC LINES OF FORCEPROPERTIES OF ELECTRIC LINES OF FORCE

Start from a positive charge and end in a negative charge.Start from a positive charge and end in a negative charge. The tangent to it at any point gives the direction of electric The tangent to it at any point gives the direction of electric

field at that point.field at that point. They never intersect each otherThey never intersect each other They tend to contract longitudinally and expand laterally.They tend to contract longitudinally and expand laterally. They always enter or emerge normal to the surface of a They always enter or emerge normal to the surface of a

charged conductor.charged conductor. They are close together in regions of strong electric field They are close together in regions of strong electric field

and far apart in regions of weak electric field.and far apart in regions of weak electric field.

WHY TWO ELECTRIC LINES OF WHY TWO ELECTRIC LINES OF FORCE NEVER INTERSECT?FORCE NEVER INTERSECT?

If they intersect two tangents can be If they intersect two tangents can be drawn from the same point( i.e. at the drawn from the same point( i.e. at the point of intersection) indicating two point of intersection) indicating two directions of electric field at the same directions of electric field at the same position which is impossible.position which is impossible.

ELECTRIC DIPOLEELECTRIC DIPOLE

Two equal and opposite point charges Two equal and opposite point charges separated by a very small distance constitute separated by a very small distance constitute an electric dipole.an electric dipole.

Electric dipole moment of a dipole is defined Electric dipole moment of a dipole is defined as the product of the magnitude of either of the as the product of the magnitude of either of the charges and the distance between the charges.charges and the distance between the charges.

Dipole moment, Dipole moment, qlp 2

ELECTRIC FIELD AT A POINT DUE TO A DIPOLEELECTRIC FIELD AT A POINT DUE TO A DIPOLE

On the axial positionOn the axial position

On the equatorial positionOn the equatorial position

lr

r

pE

lr

prE

oaxial

oaxial

when 2

4

1

2

4

1

3

222

lr

r

pE

lr

pE

oequatorial

oequatorial

when 4

1

4

1

3

22 23

TORQUE ON A DIPOLETORQUE ON A DIPOLE

= pE sin= pE sinOr Or

= p X E= p X Ewhere where pp is the electric dipole moment is the electric dipole moment

and and EE is the intensity of electric field. is the intensity of electric field.

DERIVATION (DERIVATION ( = PE sin = PE sin))Force on charge +q at A .Force on charge +q at A .

force on charge - q at B force on charge - q at B

Forces F A and FB equal Forces F A and FB equal and opposite form a couple and opposite form a couple which tends to rotate the which tends to rotate the dipole dipole

torque acting on dipole is torque acting on dipole is

AF q E

BF q E

force arm of couple

so from -------- ( 1 ) so from -------- ( 1 )

No torque acts when dipole moment aligns parallel to No torque acts when dipole moment aligns parallel to electric field ( i.e electric field ( i.e = 0 ) = 0 )

from ( 2 ) from ( 2 ) = 0 = 0

qE AC ( )1In ABCAC

ABsin AC AB sin AC l2 sin

qE l2 sin

( ) sinq l E2 pE sin ( )2 p q l dipole moment 2

pE sin 0 pE 0

ELECTRIC FLUXELECTRIC FLUXIs the total lines of force passing Is the total lines of force passing

normal to a given surface normal to a given surface

EE = E A = E A for uniform electric fieldfor uniform electric field

Electric flux is a scalar quantityElectric flux is a scalar quantity

s

E SdE

.

GAUSS’ THEOREMGAUSS’ THEOREMStates the total electric flux through a States the total electric flux through a

closed surface (surface integral of closed surface (surface integral of electric field over a closed surface) is electric field over a closed surface) is equal to 1/equal to 1/oo times the total charge times the total charge

enclosed by the surface.enclosed by the surface.

Mathematically Mathematically

enclosed

s

qSdE 0

1.

ELECTRIC FIELD AT A POINT DUE TO ELECTRIC FIELD AT A POINT DUE TO DIFFERENT CHARGE DISTRIBUTIONSDIFFERENT CHARGE DISTRIBUTIONS

E due to a point charge E due to a point charge

E due to a line of chargeE due to a line of charge

E due to a plane sheet of E due to a plane sheet of chargecharge

E due to a sphere of E due to a sphere of chargecharge

2

2int

4

1

2

2

4

1

4

1

r

qE

E

rE

r

qE

osphere

osheet

oline

opo

ELECTRIC POTENTIALELECTRIC POTENTIAL

Electric potential at any Electric potential at any point is defined as the point is defined as the work done per unit work done per unit charge in bringing a charge in bringing a positive test charge positive test charge from infinity to that from infinity to that point without any point without any acceleration.acceleration.

oq

WV

POTENTIAL DIFFERENCEPOTENTIAL DIFFERENCE

Potential difference Potential difference between two points between two points is defined as the is defined as the work done per unit work done per unit charge in carrying a charge in carrying a positive test charge positive test charge from one point to from one point to other without any other without any acceleration.acceleration.

o

ABAB q

WV

POTENTIAL ENERGY OF A POTENTIAL ENERGY OF A SYSTEM OF CHARGESSYSTEM OF CHARGES

Potential energy of a Potential energy of a system of charges is system of charges is defined as the total defined as the total work done in work done in assembling all the assembling all the charges constituting charges constituting the system from the system from infinity to their infinity to their respective positions.respective positions.

njni

jiji ij

ji

r

qqU

110 2

1

4

1

WORK DONE IN ROTATING A WORK DONE IN ROTATING A DIPOLE IN A UNIFORM DIPOLE IN A UNIFORM

ELECTRIC FIELDELECTRIC FIELD

)cos(cos 12 PEW

POTENTIAL ENERGY OF A POTENTIAL ENERGY OF A DIPOLE IN A UNIFORM ELECTRIC DIPOLE IN A UNIFORM ELECTRIC

FIELDFIELD

EPU

.

ACTION OF POINTSACTION OF POINTS

The surface charge density is not uniform in The surface charge density is not uniform in the case of uneven metal surfaces. It is the case of uneven metal surfaces. It is maximum at sharp points and hence the maximum at sharp points and hence the intensity of electric field will also be intensity of electric field will also be maximum at these points. This is known as maximum at these points. This is known as action of points.action of points.

CORONA DISCHARGECORONA DISCHARGE

When a metal with sharp points is charged, the When a metal with sharp points is charged, the sharp points acquire a high electric field and sharp points acquire a high electric field and ionizes the air molecules nearby and then ionizes the air molecules nearby and then repels them away. The charged air molecules repels them away. The charged air molecules moving away from the sharp points constitute moving away from the sharp points constitute an electric wind and the discharge of an electric wind and the discharge of electricity from sharp points like this is known electricity from sharp points like this is known as as corona discharge.corona discharge.

LIGHTNING CONDUCTORLIGHTNING CONDUCTOR Is a device made of metal with sharp points fixed on Is a device made of metal with sharp points fixed on

the top of huge buildings and earthed by thick strips the top of huge buildings and earthed by thick strips of conductor.of conductor.

They protect the building in two ways.They protect the building in two ways. They avoid the occurrence of lightning by corona They avoid the occurrence of lightning by corona

discharge and neutralizing the clouds. discharge and neutralizing the clouds. Even if lightning strikes, it provides a low resistance Even if lightning strikes, it provides a low resistance

conducting path for the charges coming from the conducting path for the charges coming from the clouds and protects the building from damage.clouds and protects the building from damage.

VAN DE GRAFFVAN DE GRAFF GENERATOR GENERATOR

Is a device used to produce very high potential by the action of points.

It works on the principle that whenever a charge is given to a hollow conductor, the charge is immediately transferred to the outer surface.

A

Van de Graff

Generator

CAPACITANCECAPACITANCE The ratio of electric charge to electric The ratio of electric charge to electric

potential of a conductor or a device is potential of a conductor or a device is called capacitancecalled capacitance

Capacitance C = Q/VCapacitance C = Q/V Unit is farad (F)Unit is farad (F) 1 farad = 1 coulomb / 1 volt1 farad = 1 coulomb / 1 volt

PRINCIPLE OF A CAPACITORPRINCIPLE OF A CAPACITOR

Capacitor is based on the principle that Capacitor is based on the principle that the capacitance of an isolated charged the capacitance of an isolated charged conductor increases when an uncharged conductor increases when an uncharged earthed conductor is kept near it and the earthed conductor is kept near it and the capacitance is further increased by capacitance is further increased by keeping a dielectric medium between the keeping a dielectric medium between the conductors.conductors.

CAPACITANCE OF A PARALLEL CAPACITANCE OF A PARALLEL PLATE CAPACITORPLATE CAPACITOR

Electric field between the plates,Electric field between the plates,

E = E = //00

But But =Q/A=Q/A

E=Q/AE=Q/A00

Potential difference between the two Potential difference between the two plates , V = Ed = Qd/A plates , V = Ed = Qd/A 00

Capacitance, C = Q/VCapacitance, C = Q/V

C=A C=A 00/d/d

CAPACITANCE OF A PARALLEL CAPACITANCE OF A PARALLEL PLATE CAPACITOR WITH A PLATE CAPACITOR WITH A

DIELECTRIC SLABDIELECTRIC SLABWhen a dielectric slab is kept between the plates When a dielectric slab is kept between the plates

COMPLETELYCOMPLETELY filling the gap filling the gap

E’ = EE’ = E00/K where K is the dielectric constant of the /K where K is the dielectric constant of the

medium.medium.

Potential difference Potential difference

V’ = E’d = EV’ = E’d = E00d/K=Qd/K d/K=Qd/K 00AA

Capacitance C’ = Q/V’ = K Capacitance C’ = Q/V’ = K 00A/d = KCA/d = KC

when a dielectric medium is filled between the plates when a dielectric medium is filled between the plates of a capacitor, its capacitance is increased K times.of a capacitor, its capacitance is increased K times.

CAPACITANCE OF A PARALLEL CAPACITANCE OF A PARALLEL PLATE CAPACITOR WITH A PLATE CAPACITOR WITH A

DIELECTRIC SLABDIELECTRIC SLAB When a dielectric slab is kept between the plates When a dielectric slab is kept between the plates

PARTIALLYPARTIALLY filling the gap filling the gap

Ktd

AC

11

" 0

CAPACITANCE OF A PARALLEL CAPACITANCE OF A PARALLEL PLATE CAPACITOR WITH A PLATE CAPACITOR WITH A

METAL SLAB OF THICKNESS tMETAL SLAB OF THICKNESS t

td

AC

0"

COMBINATION OF CAPACITORSCOMBINATION OF CAPACITORSSERIES COMBINATIONSERIES COMBINATION

When capacitors are combined in When capacitors are combined in series, the reciprocal of effective series, the reciprocal of effective capacitance capacitance

PARALLEL COMBINATIONPARALLEL COMBINATION

When capacitors are combined in When capacitors are combined in series, the effective capacitanceseries, the effective capacitance

ns CCCC

1...........

111

21

np CCCC ...........21

DEFINE DIELECTRIC CONSTANT ON THE DEFINE DIELECTRIC CONSTANT ON THE BASIS OF CAPACITANCE OF A PARALLEL BASIS OF CAPACITANCE OF A PARALLEL

PLATE CAPACITORPLATE CAPACITOR Dielectric constant of a Dielectric constant of a

medium is defined as medium is defined as the ratio of the the ratio of the capacitance of a capacitance of a capacitor completely capacitor completely filled with the medium filled with the medium to the capacitance of the to the capacitance of the capacitor without any capacitor without any dielectric.dielectric.

o

m

C

CK

DIELECTRIC STRENGTHDIELECTRIC STRENGTH

Dielectric strength of a dielectric Dielectric strength of a dielectric is the maximum electric field that is the maximum electric field that can be applied to it beyond which can be applied to it beyond which it breaks down.it breaks down.

PRACTICE PROBLEMSPRACTICE PROBLEMS

Calculate the number of electrons in excess in Calculate the number of electrons in excess in a body with 1 coulomb of negative charge.a body with 1 coulomb of negative charge.

Q = neQ = ne Q = 1CQ = 1C e = 1.6 X 10e = 1.6 X 10-19-19CC n = Q/e= 1/(1.6 X 10n = Q/e= 1/(1.6 X 10-19-19C) = 6.25 X 10C) = 6.25 X 101818