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: