Question

Statement I: Electric field is always directed perpendicular to an equipotential surface.
Statement II: Equipotential surface is a surface on which at each point potential is same.

• A. If both statements are true and statement II is the correct explanation of statement I.
• B. If both statements are true but statement II is not the correct explanation of statement I.
• C. If statement I is true but statement II is false.
• D. If both statements are false.

Answer 1

Answer: (B)

On equipotential surface, the potential at each point is same throughout.
Let $\vec{E}$ be electric field of a point on equipotential surface. Then small work done in moving a test charge $q_0$ through a small displacement along the surface,
$dW=\vec{E}\cdot d\vec{r}=\left(q_0\vec{E}\right)\cdot d\vec{r}$
Since work in moving a test charge along an equipotential surface is always zero.
$\left(-q_0\vec{E}\right)\cdot d\vec{r}=0\text{ or }\vec{E}.d\vec{r}=0$
Hence, electric field is directed perpendicular to the surface.