Question

Charges $+ q$ and $- q$ are placed at points $A$ and B respectively which are a distance $2 L$ apart, $C$ is the mid point of $A$ and $B$. The work done in moving a charge $+ Q$ along the semicircle CRD is :-

• A. $-\frac{ qQ }{6 \pi \in_{0} L }$
• B. $\frac{ qQ }{4 \pi \in_{0} L }$
• C. $\frac{ qQ }{2 \pi \in_{0} L }$
• D. $\frac{ qQ }{6 \pi \in_{0} L }$

Answer 1

Answer: (A)

$U_{i}=\frac{k q Q}{L}-\frac{k Q q}{L}=0$
$U_{f}=\frac{k q Q}{3 L}-\frac{k Q q}{L}=-\frac{2}{3} \frac{k Q q}{L}$
So, $W=U_{f}-U_{i}=-\frac{2}{3} \frac{k Q q}{L}=-\frac{Q q}{6 \pi \varepsilon_{0} L}$