StemCET Logo

Physics Question 35 – JEE-MAIN 2025

← Back
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.

Recall the properties of the electric field and potential inside a uniformly charged spherical shell.

Step 1: Analyze Electric Field and Potential inside a Spherical Shell✦ Active

Inside a uniformly charged spherical shell, the electric field E is zero. Since the electric field is the negative gradient of the potential (E=−dVdr), if E=0, then dVdr=0. This implies that the electrostatic potential V is constant everywhere inside the shell. This constant potential is equal to the potential on the surface of the shell. Therefore, Reason R is true.

Step 2: Analyze Work Done in an Electrostatic Field○ Expand

The work done W in moving a test charge q0 between two points A and B in an electrostatic field is given by W=q0(VA−VB). Since the potential V is constant inside the uniformly charged spherical shell (as established in Step 1), for any two points A and B inside the shell, VA=VB. Thus, VA−VB=0, which means W=0. Therefore, Assertion A is true.

Step 3: Evaluate the Relationship between Assertion and Reason○ Expand

Reason R states that the potential inside the shell is constant. This constancy of potential directly implies that the potential difference between any two points inside is zero. Consequently, the work done in moving a charge between these points is zero, which is what Assertion A states. Hence, Reason R is the correct explanation for Assertion A.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.