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Three concentric circular arcs, each of radius R, are centred at the same point. Their charges are +Q, -2Q and +3Q respectively. Find the net electric potential at the common centre of curvature.

1. Q / (2*pi*e0*R)
2. Q / (4*pi*e0*R)
3. 2Q / (pi*e0*R)
4. Q / (pi*e0*R)

Correct answer: Q / (2*pi*e0*R)

Solution

Potential at the centre due to a charge q spread on an arc of radius R is V = q / (4*pi*e0*R), independent of how the charge is distributed along the arc (all charge is at distance R). The total charge is +Q - 2Q + 3Q = +2Q. Hence V_net = (2Q) / (4*pi*e0*R) = Q / (2*pi*e0*R).

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