JEE Main 2025 — Electrostatics Question with Solution

$$\text{Assertion A:}$$

For a uniformly charged spherical shell, Gauss's law tells us that the electric field inside the shell is zero.

Since the electric field $$\vec{E}$$ is zero everywhere inside, the potential $$V$$ must be constant.

Work done in moving a charge from one point to another in an electric field is given by the difference in potential energy, which is $$q(V_B-V_A)$$.

If the potential difference $$V_B-V_A$$ is zero (because the potential is constant), then the work done is zero, regardless of the path taken.

Therefore, Assertion A is true.

$$\text{Reason R:}$$

It states that the electrostatic potential inside a uniformly charged spherical shell is constant and equal to that on its surface.

This is correct because the electric field inside is zero, ensuring that the potential remains uniform inside.

Thus, Reason R is also true.

$$\text{Relationship between A and R:}$$

The work done on a test charge moving inside the shell being zero is a direct consequence of the fact that the potential is constant inside.

Hence, Reason R correctly explains why the work done (Assertion A) is zero.

Given this analysis, the correct answer is:

Option B

"Both A and R are true and R is the correct explanation of A."