Question

Assertion (A): Work done to move a charge between two points is zero inside a uniformly charged shell.
Reason (R): Potential inside a uniformly charged shell is constant and equal to the potential at its surface.

• A. Both (A) \& (R) are correct, and Reason is the correct explanation of (A).
• B. Both (A) \& (R) are correct but R is not correct explanation of A.
• C. A is correct and R is incorrect
• D. A is correct and R is correct

Hint:

For problems involving spherical symmetry and uniform charge distributions, remember that the electric field inside a uniformly charged shell is zero, which leads to constant potential within the shell.

Answer 1

The Correct Option is A

We are given two statements:
Assertion (A): Work done to move a charge between two points is zero inside a uniformly charged shell.
Reason (R): Potential inside a uniformly charged shell is constant and equal to the potential at its surface.

Step 1: Verifying Assertion (A)
The work done to move a charge between two points is zero when the points lie within a region of constant potential.
According to Gauss's Law, the electric field inside a uniformly charged spherical shell is zero, meaning there is no force acting on the charge inside the shell.
Since there is no force, no work is done in moving the charge inside the shell.
Therefore, assertion (A) is correct.
Step 2: Verifying Reason (R)
The potential inside a uniformly charged spherical shell is constant and equal to the potential at its surface.
This is a consequence of the fact that the electric field inside a spherical shell is zero, and therefore, the potential inside must be uniform.
The potential inside the shell is the same as the potential on the surface of the shell.
Therefore, reason (R) is also correct.
Step 3: Relation between Assertion and Reason
Since both assertion (A) and reason (R) are correct and the reason explains the assertion, the correct option is (1).