Question

A point charge $q$ is at centre of an unchanged spherical conducting shell of inner radius $a$ and outer radius $b$ . Work needed to move the charge out to infinity will be

• A. $\frac{q^2}{4\pi {\epsilon }_0}\left(\frac{1}{a}-\frac{1}{b}\right)$
• B. $\frac{1}{8\pi {ϵ}_0}\frac{q^2}{a}$
• C. $\frac{q^2}{8\pi {ϵ}_0}[\frac{1}{b}-\frac{1}{a}]$
• D. $\frac{q^2}{8\pi {ϵ}_0}[\frac{1}{a}-\frac{1}{b}]$

Answer 1

The correct option is A $\frac{q^2}{4\pi {\epsilon }_0}\left(\frac{1}{a}-\frac{1}{b}\right)$

$ui=\frac{-k{q}^2}{a}+\frac{k{q}^2}{b}$

$=k{q}^2(\frac{1}{b}-\frac{1}{a})$

$uj=0$

$w=uj-ui$

$=k{q}^2(\frac{1}{a}-\frac{1}{b})$

$=\frac{q^2}{4\pi {\epsilon }_0}(\frac{1}{a}-\frac{1}{b})$

Hence, option $A$ is correct answer.