Elektric Potensial

ElectricPotential

Electric PotentialPotentialDifferenceandElectric PotentialPotentialDifferencesina UniformElectricFieldElectricPotentialandPotential EnergyDuetoPointChargesObtainingtheValueofthe ElectricFieldfromtheElectric PotentialElectricPotentialDueto ContinuousChargeDistributionsElectricPotentialDuetoa ChargedConductor

PotentialDifferenceandElectric Potential

Whenchargeismovedintheeld by force,theworkdonebytheeldequaltothe negativeoftheworkdonebyforcecausingthedisplacementFor small displacement ds, the work by field is

It causes the potential energy of the field reduce by:

Foranite displacementof thecharge fromapointA toapointB

PotentialDifferenceandElectric Potential

ThepotentialenergyperunitchargeU/q0 is independentof thevalueofq0 Thisis calledtheelectricpotential (orsimplythepotential)V

Thepotentialdifference betweenanytwopointsA andB

Electric potential at an arbitrary point in an electric field equals the work required per unit charge to bring a positive test charge from infinity to that point.

The unit: joules per coulomb or volt (v)

Another unit:

POTENTIAL DIFFERENCES IN A UNIFORM ELECTRIC FIELD

If q0 moves from A to B, the change in potential energy is

If q0 positive, is negative, the positive charge losses its potential energy when moving in the direction of electric field.

If q0 negative , is positive, A negative charge gains electric potential energy when it moves in the direction of theelectric field

EquipotentialThenameequipotential surface isgiven toany surface consistingofa continuousdistributionofpointshavingthesame electricpotentialAuniformelectric elddirectedalongthepositivex axis.PointB isatalowerelectric potentialthanpointA.PointsB andC areatthesame electricpotential.

ELECTRIC POTENTIAL AND POTENTIAL ENERGYDUE TO POINT CHARGESGeneralexpressionforpotentialdifference:

Thequantityin right hand canbeexpressedas

And

If

ELECTRIC POTENTIAL AND POTENTIAL ENERGYDUE TO POINT CHARGES(2)Foragroupofpointcharges,V ata point is

Potential energy of two-charge system

OBTAINING THE VALUE OF THE ELECTRIC FIELDFROM THE ELECTRIC POTENTIAL The potentialdifferencedV between two pointsadistanceds apartas

If V(x,y,z) , then E is

Example

Example (2)

ELECTRICPOTENTIAL DUE TO CONTINUOUS CHARGEDISTRIBUTIONS

The electricpotentialdV atsomepointP duetothechargeelementdq is

The total of V is

Example

The electric potential at P

Example(2)

ELECTRICPOTENTIAL DUE TO CONTINUOUS CHARGEDISTRIBUTIONS

ELECTRIC POTENTIAL DUE TO ACHARGED CONDUCTORWhen a conductor in equilibrium, the potential differencebetweenA andB isnecessarilyzero: