Question

A point charge $q$ is surrounded by eight identical charges at a distance $r$ as shown in figure. How much work is done by the forces of electrostatic repulsion when the point charge at the center is removed to infinity?

• A. $\frac{8q^2}{4\pi {\epsilon }_{0}r}$
• B. $\frac{18q^2}{4\pi {\epsilon }_{0}r}$
• C. $\frac{64q^2}{4\pi {\epsilon }_{0}r}$
• D. Zero

Answer 1

The correct option is A $\frac{8q^2}{4\pi {\epsilon }_{0}r}$

Work required to move charge $q$ to $\infty$ is

$W=-q(V_f-V_i)=-q(0-V_i)$

$=q\left(\frac{8kq}{r}\right)$

$\therefore W=\frac{8q^2}{4\pi {\epsilon }_{0}r}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.