Four charges are at the corners of a square as shown in the figure. Corners A and D have equal charge, while both B and C have a charge of +1 C. What is the charge on A so that the force on B is zero ?

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Charge q at A and D must be negative (to oppose the repulsion from C). Let $∣ q ∣ = Q$ and side be a.

On B: attractions from A and D have magnitude $k Q / a^{2}$ along BA and BD. Repulsion from C (+1 C) has magnitude $k / (2 a^{2})$ along the diagonal, i.e. components $k / (22 a^{2})$ along BA and BD.

$\frac{k Q}{a ^{2}} = \frac{k}{2 2 a ^{2}} \Rightarrow Q = \frac{1}{2 2} \approx 0.35$ . Hence q = -0.35 C, (C).

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