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Q.

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

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a

$\frac{3 Q}{32 π ε_{0} R}$

b

none of these

c

$\frac{Q}{2 π ε_{0} R}$

d

$\frac{5 Q}{12 π ε_{0} R}$

answer is A.

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Detailed Solution

Charge can be considered as located at a distance R from the center. Total charge is $(Q - 2 Q + 3 Q) = 2 Q$

Hence $V = \frac{1}{4 π ε_{0}} \frac{2 Q}{R} = \frac{Q}{2 π ε_{0} R}$

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