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 0.134 N when their center-to-center separation is 68.5 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 0.0527 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge in coulombs on one of them and (b) the positive charge in coulombs on the other?

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Explanation / Answer

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Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.132 N when their center-to-center separation is 54.2 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 0.0271 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge in coulombs on one of them and (b) the positive charge in coulombs on the other?   

answer

two charges: +q1 and -q2

F = 0.132 N, d = 54.2 cm.

F = kq1q2/d2, so q1q2 = Fd2/k = 7.95*10-12 C2 (1)

later: q = (q1 - q2)/2, F' = 0.0271 N

F' = kq2/d2

q2 = F'd2/k

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

q1 - q2 = 2d?(F'/k) = 1.88*10-6 C

q1 = q2 + 1.88*10-6 C

plug it into (1)

q22 + 1.88*10-6 q2 - 7.95*10-12 C2 = 0

solve it and get

q2 = 2.03*10-6 C

q1 = 3.91*10-6 C

answer: (a) the negative charge = -2.03*10-6 C; (b) the positive charge = 3.91*10-6 C

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