Question

A point charge $q$ is brought form infinity and is placed at the centre of a conducting neutral spherical shell of inner radius $a$ and outer radius $b,$ then work done by external agent is:

• A. $0$
• B. $\frac{k{q}^2}{2b}$
• C. $\frac{k{q}^2}{2b}-\frac{k{q}^2}{2a}$
• D. $\frac{k{q}^2}{2a}-\frac{k{q}^2}{2b}$

Answer 1

The correct option is A $0$

$v_i=\frac{-q}{4\pi {\epsilon }_{0}a}$

$v_0=\left(\frac{q}{4\pi {\epsilon }_{0}b}\right)$

$v=\frac{q}{4\pi {\epsilon }_0}\left(\frac{1}{b}-\frac{1}{a}\right)$

$W=E_p=qv=\frac{q^2}{4\pi {\epsilon }_0}\left(\frac{1}{b}-\frac{1}{a}\right)$