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**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?

## Homework Equations

[itex]V=- \int E \cdot dl[/itex]

## 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?

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