Question

A very very thin charged shell is set into spin (at some rate linearly increasing with time ). Calculate the electric field inside ? 

Answer 1

The electric field inside a shell of radius $R$ and surface charge $\sigma$ at distance $x$ from the centre is

$$E=\frac{1}{4\pi\epsilon_0}\frac{\sigma\pi R^2}{x^2}=\frac{\sigma R^2}{4\epsilon_0x^2}.$$

The field is 0 at the centre.