Question

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

Hint: The charge placed inside the shell is given, we shall find the net charge outside the shell by calculating the difference between the charge given and the charge placed within the shell. This is based on the distribution of charges on a conducting spherical shell given by the combination of electrostatic forces and Gauss’s law.

Complete step-by-step answer:
If a spherical conducting shell carries a negative charge like -3C, it can be expected that the excess electrons mutually repel each other and become uniformly distributed over the surface of the shell. The electric field lines produce outside a charge distribution like this will be pointed towards the surface of the conductor. As the excess electrons are free to move through the conductor, the parallel components of the field may cause redistribution of charges on the shell.
The charges distributed on different faces because of induction is shown in the picture

From the question, we know charge on the inner surface of the shell is +3C
Therefore, the net charge on the outer surface will be $10C-3C=7C$
The distribution of charges will be uniform on the inner surface only if the charge is placed at center, or else it would be nonuniform. The charges on the outer surface will be uniformly distributed because the displacement of the charges on the inner surface does not affect the charges on the outer surface.
Therefore, the correct answers for the given question are options (A) and (D).

Note: If a conductor is not uniformly shaped, the distribution will also be non uniform. The charges will accumulate to a maximum at a pointed end or where the radius or curvature is maximum. It is also said that charged conductors with sharp points on the surface will lose their charge rapidly.