Question

A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R at a distance of R from the centre of the shell. The electric potential at the centre of shell will be $\frac{1}{4\pi {ϵ}_0}$ times:

• A. $\frac{q}{2R}$
• B. $\frac{4q}{3R}$
• C. $\frac{5q}{6R}$
• D. $\frac{2q}{3R}$

Answer 1

The correct option is C $\frac{5q}{6R}$

Charge of -q will be induced on the the inner surface and +q on the outer surface
$V=V_1+V_2+V_3=\frac{1}{4\pi {ϵ}_0}[\frac{q}{R}-\frac{q}{2R}+\frac{q}{3R}]$
$V=\frac{1}{4\pi {ϵ}_0}\left[\frac{6q-3q+2q}{6R}\right]$
$V=\frac{1}{4\pi {ϵ}_0}\left[\frac{5q}{6R}\right]$