Question

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

• A. $\frac{Q}{2 \pi \varepsilon_{0} R}$
• B. $\frac{5 Q}{12 \pi \varepsilon_{0} R}$
• C. $\frac{3 Q}{32 \pi \varepsilon_{0} R}$
• D. none of these

Answer 1

Answer: (A)

Charge can be considered as located at a distance $R$ from the center. Total charge is $(Q-2 Q+3 Q)=2 Q$
Hence $V=\frac{1}{4 \pi \varepsilon_{0}} \frac{2 Q}{R}=\frac{Q}{2 \pi \varepsilon_{0} R}$