Question

What is the electric flux through the surface S in vacuum?

Answer 1

The electric flux:

1. The electric flux over a closed surface is defined by Gauss law as the ratio of the total net charge enclosed inside the surface to the medium's permittivity.
2. The expression for electric flux through a closed surface is,

${\varphi }_E=\frac{Q_{net}}{{\epsilon }_0}$ here $Q_{net}$ is net charge (sum of all charges within the surface) and ${\epsilon }_0$ is the permittivity of free space.

3.The total net charge is the sum of all individual charges contained within the surface.

$Q_{net}=(+2q-q)$

$Q_{net}=q$

4. As a result, the electric flux is given by

${\varphi }_E=\frac{q}{{\epsilon }_0}$

Hence, the electric flux through the surface S in a vacuum is Gauss' Law ${\varphi }_E=\frac{q}{{\epsilon }_0}$.