Question 160 of 311
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason 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 : 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
Show answer and solution
Answer: (B) Both and are true and is the correct explanation of
For a uniformly charged spherical shell:
- The electric field inside the shell is zero everywhere (from Gauss's law)
* When the electric field is zero, no work is done in moving a charge
- Since work - force displacement, and force - q̧E (where E - 0), work - 0
- The potential inside is constant and equal to the value at the surface
Assertion A is correct: Since the electric field is zero everywhere inside the shell, no work is done moving a charge between any two points, regardless of path.
Reason R is correct: The potential inside a uniformly charged spherical shell is indeed constant and equal to the value at the surface.
Does R explain ? Yes, because:
- Constant potential means zero electric field (since )
- Zero electric field means no force on a test charge
- No force means no work done in moving the charge
Therefore, opxion (2) is correct: Both A and R are true and R is the correct explanation of A.
- The electric field inside the shell is zero everywhere (from Gauss's law)
* When the electric field is zero, no work is done in moving a charge
- Since work - force displacement, and force - q̧E (where E - 0), work - 0
- The potential inside is constant and equal to the value at the surface
Assertion A is correct: Since the electric field is zero everywhere inside the shell, no work is done moving a charge between any two points, regardless of path.
Reason R is correct: The potential inside a uniformly charged spherical shell is indeed constant and equal to the value at the surface.
Does R explain ? Yes, because:
- Constant potential means zero electric field (since )
- Zero electric field means no force on a test charge
- No force means no work done in moving the charge
Therefore, opxion (2) is correct: Both A and R are true and R is the correct explanation of A.