Question

Figure shows three circular arcs, each of radius R and total charge as indicated. The net electric potential at the centre of curvature is?

• A. $\frac{Q}{2\pi {\epsilon }_{0}R}$
• B. $\frac{Q}{3\pi {\epsilon }_{0}R}$
• C. $\frac{2Q}{\pi {\epsilon }_{0}R}$
• D. $\frac{Q}{\pi {\epsilon }_{0}R}$

Answer 1

The correct option is C $\frac{2Q}{\pi {\epsilon }_{0}R}$

Radius $=R$

The net electric potential at the centre of curvature $=$ The distance from each charge to centre in $R$ as the potential is a scalar quantity so net potential at centre is -

$V=V_Q+V_{-2Q}+V_{3Q}$

$=\frac{1}{4\pi {ϵ}_0}[\frac{Q}{R}+\frac{-2Q}{R}+\frac{3Q}{R}]$

$=\frac{2Q}{4\pi {ϵ}_{0}R}$

$=\frac{2Q}{\pi {ϵ}_{0}R}$