1. Electric potential inside a conductor / outside a coaxial cable Electric Potential inside a conductor(spherical) is a constant, although electric field is zero. How does that make sense given: Given [itex]V=- \int E \cdot dl[/itex]? The integral should be 0. Even if you consider constants of integration, shouldn't they drop off because the integral is from the radius to 0? Given that potential is non-zero inside a conductor, does the same hold true outside a coaxial cable? A Gaussian surface around the cable shows that the electric field outside the cable is 0. Do we have the same case where the potential is non-zero outside of the cable? 2. Relevant equations [itex]V=- \int E \cdot dl[/itex] 3. The attempt at a solution The problem statement is my attempt at the solution. More of a lack of confusion than an actual problem. Edit: To clarify, this makes sense in reverse: E = del(V). Derivative of a constant is 0. How did that constant get there in the first place though?