Electric Potential Potential Difference and Electric Potential Potential

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 to a point B displacement of the charge from a point A

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 negative , is positive, A negative charge gains electric potential energy when it moves in the direction of the 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.

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 ENERGY DUE TO POINT CHARGES • General expression for potential differenc e: • The quantity in can be expressed as • And • If right hand

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 d. V points a distance ds apart as • If V(x, y, z) , then E is between two

Example

Example (2)

ELECTRIC�POTENTIAL DUE TO CONTINUOUS CHARGE DISTRIBUTIONS • The electric potential d. V due to the charge element dq is • The total of V is at some point P

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: