Question

Calculate the ratio of flux through surface $S_1$ and $S_2$. If another charge -3Q is placed at C. What will be the flux through $S_1$ and $S_2$?

Answer 1

Using gauss law,
$\varphi =\frac{q}{{ϵ}_0}$
$\frac{{\varphi }_1}{{\varphi }_2}=\frac{\frac{Q}{{ϵ}_0}}{\frac{(2Q+Q)}{{ϵ}_0}}=\frac{Q}{3Q}=\frac{1}{3}$
When -3Q is placed at C,
$\frac{{\varphi }_1}{{\varphi }_2}=\frac{\frac{Q}{{ϵ}_0}}{\frac{(3Q-3Q)}{{ϵ}_0}}=\infty$