JEE Physics 2024 Question with Solution

Given: Charges $5Q$ and $-2Q$ are at $(3a,0)$ and $(-5a,0)$ respectively. A sphere of radius $4a$ is centered at the origin.

Find: The electric flux through the sphere.

Use Gauss's Law. According to Gauss's law,

$$\Phi = \frac{q_{\text{enclosed}}}{\varepsilon_0}$$

The electric flux through any closed surface depends only on the net charge enclosed by that surface.

The sphere extends from $x=-4a$ to $x=+4a$.

• Charge $-2Q$ at $x=-5a$ is outside the sphere because $|-5a| > 4a$.
• Charge $5Q$ at $x=+3a$ is inside the sphere because $|3a| < 4a$.

Hence, the enclosed charge is

$$q_{\text{enclosed}} = 5Q$$

Applying Gauss's law,

$$\Phi = \frac{q_{\text{enclosed}}}{\varepsilon_0} = \frac{5Q}{\varepsilon_0}$$

Therefore, the electric flux through the sphere is $\frac{5Q}{\varepsilon_0}$. The correct option is B.

Given: A sphere of radius $4a$ is centered at the origin, with charges at $x=3a$ and $x=-5a$.

Find: The electric flux through the sphere.

For flux through a closed surface, only charges inside the surface matter. Since $3a$ lies within $\pm 4a$, the charge $5Q$ is enclosed. Since $-5a$ lies outside $\pm 4a$, the charge $-2Q$ is not enclosed.

So directly,

$$\Phi = \frac{5Q}{\varepsilon_0}$$

Therefore, the correct option is B.