Question

A conducting spherical shell of inner radius $2R$ and outer radius $3R$ has a positive point charge $q$ located at its centre. What is the electric potential at point $P$, which is at a distance $\frac{6}{7}R$ from its centre as shown in the figure.

• A. $\frac{1}{4\pi\varepsilon_{0}} \frac{q}{3R}$
• B. $\frac{1}{4\pi\varepsilon_{0}} \frac{q}{2R}$
• C. $\frac{1}{4\pi\varepsilon_{0}} \frac{q}{R}$
• D. $\frac{1}{4\pi\varepsilon_{0}} \frac{6q}{7R}$

Answer 1

Answer: (C)

$\frac{1}{4\pi\varepsilon_{0}} \frac{q}{R}$

Answer 2

The electric potential at point $P$ is $V_{P} = \frac{1}{4\pi\varepsilon_{0}} \left(\frac{q}{\frac{6}{7}R} - \frac{q}{2R} + \frac{q}{3R}\right)$ $= \frac{q}{4\pi\varepsilon_{0}R} \left(\frac{7-3+2}{6}\right) = \frac{1}{4\pi\varepsilon_{0}} \frac{q}{R}$