Question

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

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

Answer 1

Answer: (B)

$W=-q\left(V_{f}-V_{i}\right)=-q\left(V_{\infty}-V_{i}\right)=+q V_{i}$
$V_{i}=8 .\frac{k q^{2}}{r}=\frac{8 q^{2}}{4 \pi \varepsilon_{0} r}$
$W=\frac{+8 q^{2}}{4 \pi \varepsilon_{0} r}$