Question

In the shown figure a hemisphere is placed and two charges $3q$ and $9q$ are placed symmetrically about centre $O.$ Net electric flux over curved surface is given as $\frac{N_{1} q}{N_{2} \epsilon _{0}},$ where $N_{1}$ and $N_{2}$ are lowest possible integers then value of $N_{1}+N_{2}$ is :

Answer 1

According to Gauss's law of electrostatics, the net flux passing through the surface of hemisphere will be
$\phi=\frac{\left(9 + 3\right) q}{ϵ_{0}}$
Due to symmetry, the flux passing through the curved surface will be halfof the net flux. So,
$\phi=\frac{\left(9 + 3\right) q}{2 ϵ_{0}}=\frac{6 q}{ϵ_{0}}$