Question

A charge $Q$ is placed at the center of an imaginary hemispherical surface. Using symmetry arguments and Gauss's law, find the flux of the electric filed due to this charge through the surface of the hemisphere

Answer 1

We know: For a spherical surface

Flux $=\oint \overrightarrow{E}ds=\frac{q}{{ϵ}_0}$ [by Gauss law]

Hence for a hemisphere, $=$ total surface area is half of that of the sphere.

So, the net flux due to the hemispherical surface will be:

$=\frac{q}{{\in }_0}\times \frac{1}{2}=\frac{q}{2{\in }_0}$