A spherical conducting shell of inner radius `R_(1)` and outer radius `R_(2)` has charge Q. Now a charge q is placed inside the shell but not at centre then surface charge densities with their nature on inner and outer surfaces of shell are respectively.

Options

A. `(q)/(4pir_(1)^(2))` and `(Q)/(4pi r_(2)^(2))`
B. `(-q)/(4pir_(1)^(2))` and `(Q+q)/(4pi r_(2)^(2))`
C. `(q)/(4pir_(1)^(2))` and `(Q-q)/(4pi r_(2)^(2))`
D. 0 and `(Q-q)/(4pi r_(2)^(2))`

Answer

C

Explanation

Since the charge -q is placed at the centre of the shell, therefore it will induce a charge +q on the inner surface and charge -q on the outer surface of the shell.
`:.` Surface charge density on the inner surface of the shell,
`sigma = (q)/(4pi r_(1)^(2))`
Total charge on the outer surface of the shell `= Q - q`
`:.` Surface charge density on the outer surface of the shell,
`sigma_(2) = (Q-q)/(4pi r_(2)^(2))`