Question

Write Gauss's law. Determine the electric field at the points which are situated outside and inside of a uniformly charged thin spherical shell. Draw necessary diagrams of Gaussian surfaces.

Answer 1

Gauss's law states that the net flux of an electric field through a closed surface is proportional to the enclosed electric charge.

$\oint \overrightarrow{E}.d\overrightarrow{A}=\frac{q_{enc}}{{ϵ}_0}$

Electric field at a point at a distance $r$ outside spherical shell is found by

$E\left(4\pi r^2\right)=\frac{q}{{ϵ}_0}$
$⟹E_{out}=\frac{q}{4\pi {ϵ}_0{r}^2}$

Electric field at a point at a distance $r$ inside spherical shell is found by

$E\left(4\pi r^2\right)=\frac{q}{{ϵ}_0}$
$⟹E_{in}=0$