Question

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

• A. A is false but R is true
• B. Both A and R are true and R is the correct explanation of A
• C. Both A and R are true but R is NOT the correct explanation of A
• D. A is true but R is false

Hint:

For problems involving charged spherical shells, remember: - Electric field inside a uniformly charged spherical shell is zero. - Potential inside is constant and equal to the potential at the surface. - Work done is zero when moving a charge in a region of constant potential.

Answer 1

The Correct Option is B

To determine the correct answer, let's analyze the assertion and the reason given:

1. 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.
2. Reason (R): Electrostatic potential inside a uniformly charged spherical shell is constant and is the same as that on the surface of the shell.

Now, let’s examine each statement:

1. The assertion states that the work done inside a uniformly charged spherical shell is zero when moving a test charge between two points. This statement is true because, according to Gauss's Law, the electric field inside a uniformly charged spherical shell is zero. Therefore, no work is done (work = force × distance) as there is no electric force acting on the test charge inside the shell.
2. The reason states that the electrostatic potential inside the shell is constant and is the same as on the surface. This is also true. The potential inside a uniformly charged spherical shell is constant because the electric field inside the shell is zero, leading to no change in potential with movement. Additionally, this potential value is equal to the potential on the surface of the shell.

Both statements are true. Furthermore, the constancy of the potential (Reason) is the explanation for why no work is done (Assertion). In electrostatics, when the potential is constant, the work done in moving a charge is zero. Hence, Reason (R) correctly explains Assertion (A).

Therefore, the correct answer is:

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

Answer 2

Understanding Assertion A: 
The work done in moving a test charge between two points in an electric field is given by: \[ W = q \Delta V \] where \(\Delta V\) is the potential difference between the two points.
For a uniformly charged spherical shell, the electric field inside is zero (by Gauss's law), and consequently, the potential is constant throughout the interior.
Therefore, \(\Delta V = 0\) between any two points inside the shell, making the work done zero regardless of the path taken.
Thus, Assertion A is true. 

Understanding Reason R: 
The electrostatic potential inside a uniformly charged spherical shell is indeed constant and equals the potential on the surface.
This is a well-known result in electrostatics, derived from the fact that the electric field inside such a shell is zero.
Hence, Reason R is also true. 

Relationship between A and R: 
Reason R directly explains why Assertion A is true.
The constant potential (Reason R) implies no potential difference, which in turn means no work is done in moving a charge between any two points inside the shell (Assertion A).
Therefore, Reason R is the correct explanation for Assertion A.