Electric Potential

Electric Potential due to Conductors

Conductors are equipotentials. Since a charge is free to move around in a conductor, no work is done in moving a charge from one point in a conductor to another. That makes it an equipotential.

We already know that electric field lines are perpendicular to equipotential surfaces so electric field lines are prependicular to the surface of a conductor.

Consider charge Q on a metallic sphere of radius R. We have already used Gauss's Law to understand the electric field. Outside the sphere, the electric field is indistinguishable from that of a point charge Q. That is

E = k Q / r2

Likewise, the potential must be indistinguishable from that of a point charge,

V = k Q / r

Inside the electric field vanishes. That means the electric potential inside the conductor is constant.

Continuous Chargesl


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(c) Doug Davis, 2002; all rights reserved