Clarification about a conductor as an equipotential.... 1. The problem statement, all variables and given/known data 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.