Question
For an infinite line of charge having charge density $\lambda $ lying along $x-$ axis, the work required in moving charge $q$ from $C$ to $A$ along arc $CA$ is :-
✓
Answer
$\mathrm{B} $ and $ \mathrm{C}$ are equipotential and field is conservative, therefore:
$\therefore \mathrm{W}_{\mathrm{CA}}=\mathrm{W}_{\mathrm{BA}^{-}}=-\int_{2 \mathrm{a}}^{\mathrm{a}} \frac{\lambda}{2 \pi \varepsilon_{0} \mathrm{r}} \mathrm{q} \mathrm{dr}=\frac{\mathrm{q} \lambda}{2 \pi \varepsilon_{0}} \operatorname{In} 2$
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