Question

What is the force on a charge placed on an equipotential surface?

• A. Zero
• B. Along the surface
• C. Perpendicular to the surface
• D. None of the above

Hint:

On an equipotential surface, the electric field and hence the force on a charge are always perpendicular to the surface. There is no force component along the surface.

Answer 1

The Correct Option is C

Step 1: Understand what an equipotential surface is
An equipotential surface is a surface where all points have the same electric potential. No work is done in moving a charge along such a surface. Key properties:
The electric field ($ \vec{E} $) is always perpendicular to the equipotential surface.
There is no component of the electric field along the surface. Step 2: Force on a charge in an electric field
The force experienced by a charge $ q $ in an electric field $ \vec{E} $ is given by:
\[ \vec{F} = q \vec{E} \] Since the electric field is perpendicular to the equipotential surface, the force on the charge will also be perpendicular to the surface. There is no component of force along the surface, because there is no electric field along the surface.
Step 3: Analyze each option (A) Zero — Incorrect. The force is not zero; it acts in a direction perpendicular to the surface.
(B) Along the surface — Incorrect. There is no electric field along the surface, so no force acts in this direction.
(C) Perpendicular to the surface — Correct. This matches the direction of the electric field.
(D) None of the above — Incorrect, as (C) is correct. Step 4: Conclusion The force on a charge placed on an equipotential surface is: $$ (C) Perpendicular to the surface $$