Electric potential inside shell

Question

Suppose we have a hollow neutral shell and $q$ charge at $r$ from its center now we take a point a someplace other than center then will electric potential change? I don't think because electric field inside shell is zero so we have constant potential

Answer 1

For any (perfect) conducting shell the electric or magnetic fields will induce some charges to move through the shell such that they cancel the fields inside. This is called a 'Faraday's cage'.

So it doesn't matter what field's or currents you apply outside of the shell, the fields inside will always cancel.

Answer 2

Imagine a hollow metallic sphere which is not charged . Now we have a point charge outside of sphere at distance r from centre of sphere we have potential say V at center of sphere , now we take another point inside shell which is not its center , Will potential change value here?

1. Since there is no charge inside, the potential inside satisfies Laplace's equation, i.e., the potential inside can have no local maxima or minima.
2. Since the sphere is a conductor, it is an equipotential surface.

It follows that the potential inside is constant.