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

Answer 1

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

Charge can be considered as located at a distance R from the center. Total charge is $(Q-2Q+3Q)=2Q$
Hence $V=\frac{1}{4\pi {\epsilon }_0}\frac{2Q}{R}=\frac{Q}{2\pi {\epsilon }_{0}R}$