Clarification about a conductor as an equipotential

[anban]

Clarification about a conductor as an equipotential...

Homework Statement

This is not a specific problem, but a general question I have.

In Griffiths 2.5 (pg. 97 for Third Edition), it states that "A conductor is an equipotential. For if a and b are any two points within (or at the surface of) a give conductor, V(a)-V(b)= -∫ E dl = 0, and hence V(a) = V(b)."

Does this apply to ANY two points within the conductor? Say the conductor is in an external E field and polarizes. If I picked a point at the pole and a point in the center, would V(a) = V(b)?

The reason I am confused is because I am associating a charge density with potential... not sure if this is alright.

Thank you.

 

[ehild]

Yes, a conductor is equipotential when it is in equilibrium. If you put a conductor into static electric field, its points are at different potential at the beginning, but the field forces the electrons to move, and they reach their equilibrium positions, where they experience zero force. And the time to reach the equilibrium is very short for a good conductor.

ehild