Question

A point charge $q_1$ is placed inside cavity $1$ and another point charge $q_2$ is inside cavity $2$. If a point charge $q$ is placed outside the conductor then the charge on outer surface of the conductor would be

• A. $Q+q_1+q_2$ and would be distributed uniformly.
• B. $Q+q_1+q_2$ and it is non-uniformly distributed.
• C. $Q+q_1+q_2$ and the distribution depends upon the locations of $q_1,q_2$ and $q$.
• D. $Q+q_1+q_2$ and its uniform or non-uniform distribution depending upon locations of $q_1$ and $q_2$.

Answer 1

The correct option is B $Q+q_1+q_2$ and it is non-uniformly distributed.


From the data given in the question,

Charges in the two cavities produce induced charges on their surfaces as the cavity is surrounded by the conducting medium.

Charge in Cavity-1 is situated at its centre and is symmetric so the charge will spread uniformly. Similarly, Charge in Cavity-2 is also present at the center so the charge distribution is uniform.

Total charge present on the outer surface is $q_1+q_2+Q$. Distribution of this charge is non uniform as the 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 but the presence of $q$ does change the distribution of charge on outer surface,still it remains non uniform.

Hence, option (a) is the correct answer.