JEE Physics 2024 Question with Solution

Given: Five charges $+q$, $+5q$, $-2q$, $+3q$, and $-4q$ are present. The closed surface $S$ encloses the charges $+q$, $+5q$, and $-2q$.

Find: The electric flux through the surface $S$.

Use Gauss's law:

$$\Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0}$$

The net enclosed charge is:

$$Q_{\text{enc}} = q + 5q - 2q = 4q$$

Substituting into Gauss's law:

$$\Phi_E = \frac{4q}{\epsilon_0}$$

Therefore, the electric flux through the surface $S$ is $\frac{4q}{\epsilon_0}$. The correct option is B.

Given: Flux through a closed surface depends only on the charge enclosed by that surface.

Find: The electric flux through $S$.

Charges outside the surface do not contribute to net flux through the closed surface in Gauss's law. So only add the enclosed charges:

$$+q + 5q - 2q = 4q$$

Hence,

$$\Phi = \frac{4q}{\epsilon_0}$$

Therefore, the correct option is B.