Five charges +q,+5 q,-2 q,+3 q and -4 q are situated as shown in the figure. The electric flux due to this configuration through the surface S is :

Electrostatics PYQ — JEE Main 2024 · 9 Apr · Shift 2 · Q68 with Solution

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Correct answer: D

For any closed surface $S$ , the net electric flux through it is

\Phi = \frac{Q_{\text{enclosed}}}{\varepsilon_0}

So we only need the net charge enclosed by surface $S$ .

From the given configuration, the charges enclosed by surface $S$ are:

+5q,\quad -2q,\quad +3q,\quad -4q

The charge $+q$ lies outside the surface, so it does not contribute to net flux through $S$ .

Q_{\text{enclosed}} = 5q - 2q + 3q - 4q

Q_{\text{enclosed}} = 2q

\Phi = \frac{2q}{\varepsilon_0}

The value $\dfrac{2q}{\varepsilon_0}$ is not present among the given options.

So the correct physical answer should be

\boxed{\frac{2q}{\varepsilon_0}}

and none of the listed options match it.

Stored correct answer is D: $\dfrac{4q}{\varepsilon_0}$ .

This does not agree with Gauss's law using the enclosed charges identified above. Hence I disagree with the stored answer.