Two identical conducting spheres, fixed in place, attract each other with an ele

Question

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.122 N when their center-to-center separation is 60.8 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0319 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude.)

Explanation / Answer

two charges: +q1 and -q2

F = 0.122 N, d = 60.8 cm.

F = kq1q2/d2, so q1q2 = Fd2/k = 5.01*10-12 C2 (1)

later: q = (q1 - q2)/2, F' = 0.0319 N

F' = kq2/d2

q2 = F'd2/k

(q1 - q2)2 = 4F'd2/k

q1 - q2 = 2d?(F'/k) = 2.29*10-6 C

q1 = q2 + 2.29*10-6 C

plug it into (1)

q22 + 2.29*10-6 q2 - 5.01*10-12 C2 = 0

solve it and get

q2 = 1.369*10-6 C

q1 = 3.659*10-6 C

answer: (a) the negative charge = -1.369*10-6 C; (b) the positive charge = 3.659*10-6 C

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