Answer to Question #129622 in Electricity and Magnetism for ABC

Question

A charged conducting sphere of radius R is embedded in a material that
is infinite in extent and has a permittivity of apsolon E. The external electric field
is uniform and has a magnitude of Eo. The sphere has a net charge of q.
Find the electric field (a) inside and (b) outside the sphere.

Answer 1

(a) inside the conducting sphere the field is zero ($E=0$ )

(b) the field created by the charge on the sphere

$\overrightarrow{E}=k\frac{q}{r^2}\cdot\frac{\overrightarrow{r}}{r}$ ($r>R$ )

The field outside the sphere

$\overrightarrow{E}_\Sigma=\overrightarrow{E}_0+k\frac{q}{r^2}\cdot\frac{\overrightarrow{r}}{r}$