A point charge `q_1` is placed inside cavity 1 and another point charge `q_2` is inside cavity 2. A point charge q is placed outside the conductor. For the situation described above, answer the following questions.

The charge on outer surface of the conductor would be

Options

A. `Q+q_1+q_2` and nonuniformly distributed
B. `Q+q_1+q_2` and its uniform or nonuniform distribution depends upon locations of `q_1 and q_2`
C. `Q+q_1+q_2` and would be distributed uniformly
D. `Q+q_1+q_2` and the distribution depends upon the locations of `q_1, q_2 , and q`.

Answer

A

Explanation

The charge distribution on various surfaces is as shown in the following figure, `-q_(1)` on the surface of cavity 1 will spread uniformly if `q_(1)` is at the centre, otherwise the distribution would be nonuniform. Same is the case with `-q_(2)` the charge appearing on outer surface of the conductor is `q_(1)+q_(2)+Q` which would be non-uniformly distributed as radius of curvature at various points of conductor's surface is different, the presence of `q_(1)` and `q_(2)` (and their location) has no effect on the distribution of charge on the outer surface. The presence of q will change the distribution of charge on outer surface, but still it remains non uniform.