Question

Given below are two statements : one is labelled a 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 but (R) is not the correct explanation of (A)
• B. (A) is correct but (R) is not correct
• C. (A) is not correct but (R) is correct
• D. Both (A) and (R) are correct and (R) is the correct explanation of (A)

Answer 1

The Correct Option is D

To solve this question, we need to analyze both the assertion and the reason provided, and determine if each statement is correct and if the reason is a valid explanation for the assertion.

1. Assertion (A): Work done by electric field on moving a positive charge on an equipotential surface is always zero.
   • An equipotential surface is defined by the property that the electric potential is constant everywhere on the surface.
   • The work done, W, when moving a charge, q, over a distance, d, in an electric field, E, is given by W = q \cdot \Delta V, where \Delta V is the change in electric potential.
   • Since \Delta V is zero on an equipotential surface, the work done, W = q \cdot 0 = 0.
   • Therefore, assertion (A) is correct.
2. Reason (R): Electric lines of forces are always perpendicular to equipotential surfaces.
   • Equipotential surfaces are perpendicular to electric field lines because the electric field is defined as the negative gradient of the electric potential.
   • This means that the direction of the maximum rate of decrease of potential is along the electric field lines, which naturally makes them perpendicular to surfaces of constant potential (equipotential surfaces).
   • Therefore, reason (R) is correct.
3. Conclusion:
   • Both the assertion and the reason are correct. Additionally, (R) explains why (A) is true, because if the field lines are perpendicular to the equipotential surface, there is no component of the field along the surface to do work.
   • Thus, the correct choice is: Both (A) and (R) are correct and (R) is the correct explanation of (A).

Answer 2

The work done by an electric field when moving a charge on an equipotential surface is zero because there is no change in electric potential energy. Electric lines of force are always perpendicular to equipotential surfaces, meaning that any movement along the surface does not alter the electric potential, confirming that no work is done.

The Correct answer is: Both (A) and (R) are correct and (R) is the correct explanation of (A)