Question

Find the potential inside and outside a spherical shell of radius R, which carries a uniform surface charge. Set the reference point at infinity

Answer 1

The electric field inside:

$$E=0$$

The electric field outside:

$$E=\frac{kq}{r^2},r>R$$

$$V(r)=-\int_\infty^rEdr=\frac{kq}{r},r>R\\V(r)=\frac{kq}{R},r<R$$