Electric Potential•Potential Difference and Electric Potential•Potential Differences in a Uniform Electric Field•Electric Potential and Potential Energy Due to Point Charges•Obtaining the Value of the Electric Field from the Electric Potential•Electric Potential Due to Continuous Charge Distributions•Electric Potential Due to a Charged Conductor

Potential Difference and Electric Potential

• When charge is moved in the field by force, the work done by the field equal to the negative of the work done by force causing the displacement

• For small displacement ds, the work by field is

• It causes the potential energy of the field reduce by:

• For a finite displacement of the charge from a point A to a point B

Potential Difference and Electric Potential

• The potential energy per unit charge U/q0 is independent of the value of q0

• This is called the electric potential (or simply the potential) V

• The potential difference between any two points A and B

• 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

Equipotential

• The name equipotential surface is given to any surface consisting of a continuous distribution of points having the same electric potential

• A uniform electric field directed along the positive x axis. Point B is at a lower electric potential than point A. Points B and C are at the same electric potential.

ELECTRIC POTENTIAL AND POTENTIAL ENERGYDUE TO POINT CHARGES

• General expression for potential difference:

• The quantity in right hand can be expressed as

• And

• If AR

ELECTRIC POTENTIAL AND POTENTIAL ENERGYDUE TO POINT CHARGES(2)

• For a group of point charges, V at a point is

• Potential energy of two-charge system

OBTAINING THE VALUE OF THE ELECTRIC FIELDFROM THE ELECTRIC POTENTIAL

• The potential difference dV between two points a distance ds apart as

• If V(x,y,z) , then E is

Example

Example (2)

ELECTRIC POTENTIAL DUE TO CONTINUOUS CHARGE�DISTRIBUTIONS

•The electric potential dV at some point P due to the charge element dq is

•The total of V is

Example

• The electric potential at P

Example(2)

ELECTRIC POTENTIAL DUE TO CONTINUOUS CHARGE�DISTRIBUTIONS

ELECTRIC POTENTIAL DUE TO ACHARGED CONDUCTOR

• When a conductor in equilibrium, the potential difference between A and B is necessarily zero: