Question

Charge + q placed at point A is a distance 2L apart from B and C is the midpoint between A and B. The work done in moving charge + Q along the semicircle CRD is .

• A. $\frac{qQ}{2\pi {\epsilon }_{0}L}$
• B. $\frac{9Q}{6\pi {\epsilon }_{0}L}$
• C. $-\frac{qQ}{6\pi {\epsilon }_{0}L}$
• D. $\frac{qQ}{4\pi {\epsilon }_{0}L}$

Answer 1

The correct option is C $-\frac{qQ}{6\pi {\epsilon }_{0}L}$

$\begin{array}{c}ui=\frac{kqQ}{l}\\ uf=\frac{kqQ}{3l}\\ w=\left(uf-ui\right)\\ =-\frac{2}{3}\frac{kqQ}{l}\\ =-\frac{qQ}{6\pi E_{0}L}\end{array}$

$\therefore$ Option $C$ is correct.