JEE Main 2024 · 27 January · evening · Single correct · +4 / −1
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero.
Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces.
In the light of the above statements, choose the most appropriate answer from the options given below :
- (a) Both (A) and (R) are correct and (R) is the correct explanation of (A)
- (b) (A) is correct but (R) is not correct
- (c) Both (A) and (R) are correct but (R) is not the correct explanation of (A)
- (d) (A) is not correct but (R) is correct
Answer and solution
Answer (a) Both (A) and (R) are correct and (R) is the correct explanation of (A)
Solution
Physics sir · 4 steps
Field perpendicular to the surface, displacement along it: the dot product F⃗· ds⃗ is zero.
- Check A. Work done by the field is W = q(V_A - V_B). On an equipotential surface V_A = V_B, so W = 0 for any path on it. A is correct.
- Check R. If the field had a component along the surface, moving along it would change the potential. Since the potential does not change along an equipotential surface, the field must be perpendicular to it. R is correct.
dW = qE⃗· ds⃗ = qE ds cos 90° = 0
- Does R explain A. Every small step ds⃗ taken on the surface is perpendicular to E⃗, so the force does no work on any step. That is exactly why the total work is zero, so R explains A.
- So. Both statements are correct and R is the correct explanation of A, which is option (a).
The idea to keep. On an equipotential surface, Δ V = 0 means zero work. The field lines being perpendicular to the surface is the reason, because the force never has a component along your motion.
Answer from the NTA final answer key. Solution by PrepWiser.