Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen. Reason R : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below.

Both A and R are true but R is NOT the correct explanation of A

Electrostatics PYQ — JEE Main 2025 · 8 Apr · Shift 2 · Q65 with Solution

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Correct answer: B

For a uniformly charged spherical shell, the electric field inside the shell is zero:

$E = 0 \quad \text{for } r<R$

where $R$ is the radius of the shell.

Work done in moving a test charge $q$ from one point to another is

$W = q \int \vec{E}\cdot d\vec{l}$

Since inside the shell $\vec{E}=0$ everywhere,

$W = q \int 0\, dl = 0$

So, the work done is zero for any path between two points inside the shell.

Hence, Assertion A is true.

The electrostatic potential inside a uniformly charged spherical shell is constant throughout the interior and equal to the potential at the surface:

$V = \frac{1}{4\pi\varepsilon_0}\frac{Q}{R} \quad \text{for } r\le R$

Thus, any two points inside the shell have the same potential.

Hence, Reason R is true.

Work done in moving a charge between two points is related to potential difference:

$W = q(V_1 - V_2)$

Since inside the shell the potential is constant,

$V_1 = V_2$

Therefore,

$W = q(V_1 - V_2)=0$

So the reason directly explains why the work done is zero.

Hence, R is the correct explanation of A.

Therefore, the correct option is:

$\boxed{\text{B}}$

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