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

Hint: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.