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/q 0 is independent of the value of q 0 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 q 0 moves from A to B, the change in potential energy is If q 0 positive, is negative, the positive charge losses its potential energy when moving in the direction of electric field. If q 0 negative, is positive, A negative charge gains electric potential energy when it moves in the direction of the electric field

Equipotential The name equipotential surface is given to any surface cons isting 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 ENERGY DUE TO POINT CHARGES General expression for potential differenc e: The quantity in right hand can be expressed as And If

ELECTRIC POTENTIAL AND POTENTIAL ENERGY DUE 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 FIELD FROM 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 A CHARGED CONDUCTOR When a conductor in equilibrium, the potential difference between A and B is necessarily zero: