Four closed surfaces and corresponding charge distributions are shown below.

Let the respective electric fluxes through the surfaces be ${\mathrm{\varphi }}_1,{\mathrm{\varphi }}_2,{\mathrm{\varphi }}_3$ and ${\mathrm{\varphi }}_4$

Given Data: Four closed surfaces and corresponding charge distributions are given.

Concept Used: Gauss Law.

Detailed Solution:

We know,

Flux through a surface is given by $\varphi =\frac{\Sigma q}{ϵ}$, where $\Sigma q$ = Total charge enclosed in a surface.

${\varphi }_1=\frac{2q}{ϵ}$

${\varphi }_2=\frac{2q}{ϵ}$

${\varphi }_3=\frac{2q}{ϵ}$

${\varphi }_4=\frac{2q}{ϵ}$

So, ${\varphi }_1={\varphi }_2={\varphi }_3={\varphi }_4$