Question

A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure. Let ${V_A}$, ${V_B}$ and ${V_C}$ be the potentials at points A, B and C respectively. Then:

A. ${V_C} > {V_B}$
B. ${V_B} > {V_C}$
C. ${V_A} = {V_B} = {V_C}$
D. ${V_A} < {V_C}$

Answer 1

We are asked to find the potentials at points A, B and C due to an electric field produced by a point charge. Recall how the potential is spread on a conducting sphere and how the potential on different points on the surface changes. And check which of the given options fits the condition.

Complete step by step answer:
Given, a hollow conducting sphere is placed in an electric field produced by a point charge placed at P. We have to find the potentials at points A, B and C which are ${V_A}$, ${V_B}$ and ${V_C}$ respectively. We observe that the given points A, B and C are on the surface of the sphere.

The sphere is a hollow conducting sphere. And for conducting spheres the points on the surface have equal potential. So, as here the points A, B and C are on the surface so the potentials of the points will also be the same. Therefore, ${V_A} = {V_B} = {V_C}$.

Hence, the correct answer is option C.

Note: Remember that the surface of a conductor is always an equipotential surface. Inside a hollow conducting sphere, there is no electric field that means the potential is constant. And also remember the work done is zero when a charge is moved between two points in an equipotential surface, as their potentials are the same.