Question

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

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

Answer 1

Answer: (C)

$-\frac{ qQ }{6 \pi \in_{0} L }$

Answer 2

$W =\Delta U = Q \left( V _{ D }- V _{ C }\right)$ here $V _{ C }=0$
$= Q \left[\frac{ q }{4 \,\pi \,\epsilon_{0}\,(3 L )}-\frac{ q }{4 \,\pi\, \in_{0}\,( L )}-0\right]=\frac{- Qq }{6\, \pi \,\in_{0} \,L }$