Question

By the gauss's theorem show that the electric field in a hollow spherical conductor is zero?

Answer 1

If a surface is chosen and it contains no charge, then the electric field is zero.

Explanation:

Gauss's Law defines a surface to establish a relationship between enclosed charge and electric field.

For the hollow spherical conductor, all charges will lie on the outer surface. If you were to take a surface that resided inside of the hollow spherical conductor, there would be no charge there. Hence, the electric field would be zero.

In terms of Gauss's Law mathematically:

`oint \ vec(E) * dvec(a) = q_"enc" / epsilon_0`

For no enclosed charge:

`oint \ vec(E) * dvec(a) = 0`

Since the area we select inside the hollow spherical conductor is some arbitrary sphere, we know that our surface has non-zero area.

Hence, the only way this is satisfied is if `E = 0`.