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Question 21.65: The initial charges on the three identical metal spheres in ......

The initial charges on the three identical metal spheres in Fig. 21-24 are the following: sphere A, Q; sphere B, -Q/4; and sphere C, Q/2, where Q = 2.00 × 10^{-14} C. Spheres A and B are fixed in place, with a center-to-center separation of d = 1.20 m, which is much larger than the spheres. Sphere C is touched first to sphere A and then to sphere B and is then removed. What then is the magnitude of the electrostatic force between spheres A and B?

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When sphere C touches sphere A, they divide up their total charge (Q/2 plus Q) equally between them. Thus, sphere A now has charge 3Q/4, and the magnitude of the force of attraction between A and B becomes

F=k \frac{(3 Q / 4)(Q / 4)}{d^2}=4.68 \times 10^{-19}\, N .

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