Question

$S_1,S_2,S_3$ are three concentric spherical shells, as shown in figure. $S_1$ and $S_2$ have charge $4Q$ and $8Q$ respectively, whereas $S_3$ is uncharged. Find the ratio of the flux passing through $S_1$ to that through $S_3$

• A. $1:3$
• B. $1:2$
• C. $2:1$
• D. $1:6$

Answer 1

The correct option is A $1:3$

According to Gauss law,

Flux passing through a closed surface is given by, $\varphi =\frac{q}{{ϵ}_o}$

where $q$ is charge enclosed in the closed surface.

Now, charge on first surface is $4Q$.

Flux through $S_1=\frac{4Q}{{ϵ}_o}$

Total charge enclosed in surface $S_3=4Q+8Q=12Q$

Flux through $S_3=\frac{12Q}{{ϵ}_o}$

Ratio of flux through $S_1$ and $S_3=\frac{4Q}{12Q}=1:3$