Question

The electrostatic potential on the surface of a charged conducting sphere is 100 V. Two statements are made in this regard

S1: At any point inside the sphere, electric intensity is zero.

S2: At any point inside the sphere, the electrostatic potential is 100 V.

Which of the following is a correct statement?

A. S1 is true but S2 is false
B. Both S1 and S2 are false
C. S1 is true, S2 is also true and S1 is the cause of S2
D. S1 is true, S2 is also true but the statements are independent

Answer 1

Both statements are true: At any point inside the charged conducting sphere, the electric intensity is zero, and the electrostatic potential is the same as on the surface, which is 100 V. This is because the sphere is an equipotential surface in electrostatic equilibrium.

Step-by-step explanation:

If the electrostatic potential on the surface of a charged conducting sphere is 100 V, it is correct to say:

S1: At any point inside the sphere, electric intensity is zero.
S2: At any point inside the sphere, the electrostatic potential is 100 V.

Statement S1 is true based on the principle that the electric field inside a conductor in electrostatic equilibrium is zero. Since electric charges reside on the surface of a conductor, no electric field lines exist inside the sphere, resulting in an electric intensity of zero.

Statement S2 is also true. Through the concept of equipotential surfaces, we know that within a conductor in electrostatic equilibrium, the potential is constant. It is the same at any point inside the conductor as it is on its surface whenever there is no electric field (since dV = -E · ds and E is zero, dV must also be zero). Therefore, the potential at any interior point is the same as on the surface, which is 100 V.

Hence, the correct statement is C. S1 is true, S2 is also true and S1 is the cause of S2.