Question

Consider three point charges $-2Q,+Q$, and $-Q$ and four closed surfaces $S_1,S_2,S_3$, and $S_4$.

Answer 1

Using Gauss's law, electric flux, $\varphi =\frac{Q_{en}}{{ϵ}_0}$ where $Q_{en}=$ charge enclosed by the surface.
A) For $S_1:Q_{en}=-2Q+Q=-Q\Rightarrow {\varphi }_1=\frac{-Q}{{ϵ}_0}$
thus, $A\to 1,4$
B) For $S_2:Q_{en}=-Q+Q=0\Rightarrow {\varphi }_2=\frac{0}{{ϵ}_0}=0$
thus, $B\to 3$
C) For $S_3:Q_{en}=-2Q+Q-Q=-2Q\Rightarrow {\varphi }_3=\frac{-2Q}{{ϵ}_0}$
thus, $C\to 2,4$
D) For $S_4:Q_{en}=0\Rightarrow {\varphi }_4=\frac{0}{{ϵ}_0}=0$
thus, $D\to 3$