For the situation shown in the figure below mark out the correct statement (s) -
.

Options

A. Potential of the conductor is `q//[4 pi epsilon_0 (d + R)]`.
B. Potential of the conductor is `q//4 pin epsilon_0 d`.
C. Potential of the conductor cannot be determined as the nature of distribution of induced charges is not known.
D. Potential at point `B` due to the induced charges is `-q R//[4 pi epsilon_0(d + R)d]`.

Answer

a.,d.

Explanation

As no charge is present inside the conductor, potential at any point inside the conductor is same as that of the potential or conductor.
So potential of the conductor = potential at the center
=`V_q + V_("induced charges")`
i.e., `V_("conductor") = q/(4 pi epsilon_0(d + R)) + 0`
As the total induced charge at conductor's surface is equal to zero, the potential at center due to the induced charges is zero. For point `B`
`V_("conductor") = V_("at point B") = V_q + V_("induced charges")
`V_("induced charges") = q/(4 pi epsilon_0 (d + R)) - q/(4 pi epsilon_0 d) = (-q R)/(4 pi epsilon_0 d (d + R))`.