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 center of the shell. Find the electric potential at the center of the shell.

• A. $\frac{1}{4\pi {\epsilon }_0}\frac{q}{2R}$
• B. $\frac{1}{4\pi {\epsilon }_0}\frac{4q}{3R}$
• C. $\frac{1}{4\pi {\epsilon }_0}\frac{2q}{3R}$
• D. $\frac{1}{4\pi {\epsilon }_0}\frac{5q}{6R}$

Answer 1

Answer: (D)

Electric potential due to point charge $=k\frac{q}{R}$

Electric potential due to inner surface of shell $=-\frac{kq}{2R}$

and electric potential due to outer surface of shell $=\frac{kq}{3R}$

$V=k\frac{q}{R}-\frac{kq}{2R}+\frac{kq}{3R}=\frac{kq}{R}[1-\frac{1}{2}+\frac{1}{3}]$

$=\frac{k5q}{6R}$