Question

State and Explain Gauss’ theorem.

Answer 1

$\underset{–}{StatementofGau{s}^{\prime }slaw}$

The total electric flux across a closed surface in an electric field is equal to $\left(\frac{1}{{ϵ}_0}\right)$ times the total charge enclosed by it.

Consider a closed surface S in an electric field. Let Q be the total charge in the volume enclosed by the surface.

$Q=\sum q_{n}where\sum q_n=q_1+q_2+q_3+-----------+q_n$

Then outward electric flux over entire area is

$\Phi =\oint \overrightarrow{E}.\overrightarrow{ds}=\frac{Q}{{ϵ}_o}$