Question

10 C charge is given to a conducting spherical shell and a −3 C point charge is placed inside the shell. For this arrangement, find the correct statement(s).

A. the charge on the inner surface of the shell will be +3C, and it can be distributed uniformly or nonuniformly.
B. the charge on the inner surface of the shell will be +3C, and it’s distribution would be uniform.
C. The net charge on the outer surface of the shell will be +7C, and it can be distributed uniformly or nonuniformly.
D. the net charge on the outer surface of the shell will be +7C, and it’s distribution would be uniform.

Answer 1

The correct statements are B and D, where the inner surface of the shell has a +3 C charge distributed uniformly and the outer surface carries a net charge of +7 C, also distributed uniformly.

Step-by-step explanation:

When a conducting spherical shell is given a 10 C charge and a −3 C point charge is placed inside, the charges inside the conductor will redistribute. The inner surface of the shell will acquire a +3 C charge to offset the −3 C charge inside, and this distribution will indeed be uniform, resulting in answer choice B being correct. Due to the redistribution, the outer surface of the shell will have a net charge of +7 C (10 C total minus 3 C on the inner surface), and since the shell is spherical and in electrostatic equilibrium, this charge will also distribute uniformly, making answer choice D correct. This is because a conducting sphere in electrostatic equilibrium is a spherical equipotential surface, meaning all excess charge resides on the outer surface and spreads out uniformly.