Question

Charge Q is distributed uniformly over a non conducting sphere of radius $R$. Find the electric potential at distance $r$ from the centre of the sphere ($r<R$). The electric field at a distance $r$ from the centre of the sphere is given as $\frac{1}{4\pi {ϵ}_0}\frac{Q}{R^3}r\hat{r}$. Also find the potential at the centre of the sphere.

Answer 1

The electric potential at a distance r from the center of a sphere of radius R where r<R and sphere is uniformly distributed with charge Q, is $V_r=\frac{KQ}{2R}(3-\frac{r^2}{R^2})=\frac{KQ(3R^2-r^2)}{2R^3}=\frac{1}{4\pi {\epsilon }_o}\frac{Q(3R^2-r^2)}{2R^3}$

At the center of a sphere, the value of R=0. So, according to formula of potential, V= $K\frac{Q}{R}$. Here R= 0. So the potential at the center will be infinite.