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. $\frac{Q}{2\pi {ϵ}_{0}R}$
• B. $\frac{Q}{4\pi {ϵ}_{0}R}$
• C. $\frac{2Q}{\pi {ϵ}_{0}R}$
• D. $\frac{Q}{\pi {ϵ}_{0}R}$

Answer 1

The correct option is A $\frac{Q}{2\pi {ϵ}_{0}R}$

The distance from each charge to center is $R$.
As the potential is a scalar quantity so net potential at center is
$V=V_Q+V_{-2Q}+V_{3Q}=\frac{1}{4\pi {ϵ}_0}[\frac{Q}{R}+\frac{-2Q}{R}+\frac{3Q}{R}]$
$=\frac{2Q}{4\pi {ϵ}_{0}R}=\frac{Q}{2\pi {ϵ}_{0}R}$