JEE Physics 2025 Question with Solution

Given: Assertion $A$ says that work done in moving a test charge between any two points inside a uniformly charged spherical shell is zero, irrespective of path.

Find: Whether Assertion $A$ and Reason $R$ are true, and whether $R$ correctly explains $A$.

Inside a uniformly charged spherical shell, the electric field is zero. Hence the electrostatic potential inside the shell remains constant and is equal to the potential at the surface.

The work done in moving a test charge $q$ between two points is

$$W = q\Delta V$$

Since the potential is constant inside the shell,

$$\Delta V = 0$$

Therefore,

$$W = q \times 0 = 0$$

So Assertion $A$ is true.

Reason $R$ is also true because the electrostatic potential inside a uniformly charged spherical shell is constant and equal to the surface potential.

Further, this constant potential directly explains why the work done is zero for motion between any two interior points.

Therefore, both $A$ and $R$ are true and $R$ is the correct explanation of $A$. The correct option is B.

Given: A test charge is moved between two points inside a uniformly charged spherical shell.

Find: The correct relation between Assertion $A$ and Reason $R$.

By Gauss's law, the electric field inside a uniformly charged spherical shell is zero. Hence no electric force acts on the test charge anywhere inside the shell.

Also, when electric field is zero throughout a region, the potential does not change from one point to another in that region. Therefore the potential inside the shell is constant and equal to the potential at the surface.

For electrostatic motion between two points,

$$W = q\Delta V$$

Because both points are at the same potential,

$$\Delta V = 0$$

So the work done is zero, independent of the path followed.

Thus Assertion $A$ is true, Reason $R$ is true, and Reason $R$ correctly explains Assertion $A$.

Hence, the correct option is B.