Electrostatics

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

ELECTRICITY PRODUCED BY RUBBING IS ELECTRICITY PRODUCED BY RUBBING IS CALLED FRICTIONAL ELECTRICITYCALLED FRICTIONAL ELECTRICITY

SINCE THE CHARGES SO PRODUCED ARE AT SINCE THE CHARGES SO PRODUCED ARE AT REST IT IS ALSO CALLED STATIC ELECTRICITYREST IT 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 according to which resinous charge was called negative charge was called negative and the other was called and the other was called positivepositive

CONSERVATION OF CONSERVATION OF CHARGESCHARGES

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 DESTROYED IN EQUAL AND OPPOSITE PAIRSPAIRS

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

1919CC)) 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 ARE PARTICLES CONSIDERED TO

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

RELATIVE PERMITIVITYRELATIVE PERMITIVITY

Is defined as the ratio of the force Is defined as the ratio of the force between two point charges between two point charges separated in vacuum to the force separated in vacuum to the force between the same two charges between the same two charges separated by the same distance separated by the same distance while kept in the medium.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 States that when there are a number of point charges, the net force on of point charges, the net force on any one of the charges is equal to any one of the charges is equal to the vector sum of the forces due to the vector sum of the forces due to the individual charges.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 One coulomb is defined as that charge which when kept one metre apart which when kept one metre apart from an equal and similar charge in from an equal and similar charge in vacuum, repels it with a force of 9 x vacuum, repels it with a force of 9 x 101099N.N.

ELECTRIC FIELDELECTRIC FIELD QualitativelyQualitatively

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

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

point is defined as the force exerted per point is defined as the force exerted per unit charge by a positive test charge kept unit charge by a positive test charge kept at that point.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 tangent to it at any point gives the direction of electric field at that point.direction of 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 move in the direction of electric field and a negative point charge will move in a a negative point charge will move in a direction opposite to the direction of direction opposite to the direction of electric field along an electric line of electric field along an electric line of force.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 Start from a positive charge and end in a

negative charge.negative charge. The tangent to it at any point gives the direction The tangent to it at any point gives the direction

of electric field at that point.of electric field at that point. They never intersect each otherThey never intersect each other They tend to contract longitudinally and expand They tend to contract longitudinally and expand

laterally.laterally. They always enter or emerge normal to the They always enter or emerge normal to the

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

ELECTRIC DIPOLEELECTRIC DIPOLE

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

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

Dipole moment, Dipole moment, qlp 2

TORQUE ON A DIPOLETORQUE ON A DIPOLE

= pE sin= pE sinOr Or

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

moment and moment and EE is the intensity of electric is the intensity of electric field. 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 and opposite form a couple which tends to couple which tends to rotate the dipole rotate the 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 No torque acts when dipole moment aligns parallel to electric field ( i.e parallel to 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 sin0 pE 0

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

passing normal to a given surface passing normal to a given surface

EE = E A = E A for uniform electric for uniform electric fieldfield

Electric flux is a scalar quantityElectric flux is a scalar quantity

s

E SdE

.

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

through a closed surface through a closed surface (surface integral of electric field (surface integral of electric field over a closed surface) is equal over a closed surface) is equal to 1/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.

ACTION OF POINTSACTION OF POINTS

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

CORONA DISCHARGECORONA DISCHARGE

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

LIGHTNING CONDUCTORLIGHTNING CONDUCTOR Is a device made of metal with sharp Is a device made of metal with sharp

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

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

corona discharge and neutralizing the corona discharge and neutralizing the clouds. clouds.

Even if lightning strikes, it provides a low Even if lightning strikes, it provides a low resistance conducting path for the charges resistance conducting path for the charges coming from the clouds and protects the coming from the clouds and protects the building from damage.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 The ratio of electric charge to electric potential of a conductor electric potential of a conductor or a device is called capacitanceor a device is called 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 PRINCIPLE OF A CAPACITORCAPACITOR

Capacitor is based on the principle Capacitor is based on the principle that the capacitance of an isolated that the capacitance of an isolated charged conductor increases when charged conductor increases when an uncharged earthed conductor is an uncharged earthed conductor is kept near it and the capacitance is kept near it and the capacitance is further increased by keeping a further increased by keeping a dielectric medium between the 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 Potential difference between the two plates , V = Ed = Qd/A two 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 When a dielectric slab is kept between the

plates plates COMPLETELYCOMPLETELY filling the gap filling the gap

E’ = EE’ = E00/K where K is the dielectric constant of /K where K is the dielectric constant of the medium.the 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 when a dielectric medium is filled between the plates of a capacitor, its capacitance is plates of a capacitor, its capacitance is increased K times.increased K times.

DIELECTRIC STRENGTHDIELECTRIC STRENGTH

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

PRACTICE PROBLEMSPRACTICE PROBLEMS

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