Question

$S_1$ and $S_2$ are two hollow concentric sphere enclosing charge Q and 2Q, respectively, as shown in fig. What is the ratio of the electric flux leaving through the surface of $S_2$ and $S_1$?

Answer 1

Using Gauss's law,
${\varphi }_1=\frac{Q}{ϵ}$ ${\varphi }_2=\frac{Q+2Q}{ϵ}$
$\therefore \frac{{\varphi }_1}{{\varphi }_2}=\frac{Q/ϵ}{3Q/ϵ}=\frac{1}{3}$