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 -0.7692 N when separated by 50 cm, center-to-center. 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 0.1298 N. What were the initial charges on the spheres? Since one is negative and you cannot tell which is positive or negative, there are two solutions.

i have posted this question and have gotten multiple wrong answers so I am making it a lot of points if you can get it!

Explanation / Answer

two charges: +q1 and -q2

F = 0.7692 N, d = 50 cm.

F = kq1q2/d2, so q1q2 = Fd2/k = 21.3*10-12 C2 (1)

later: q = (q1 - q2)/2, F' = 0.1298N

F' = kq2/d2

q2 = F'd2/k

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

q1 - q2 = 2d?(F'/k) = 3.79*10-6 C

q1 = q2 + 3.79*10-6 C

plug it into (1)

q22 + 3.79*10-6 q2 - 21.3*10-12 C2 = 0

solve it and get

q2 = 3.09*10-6 C and q1 - q2 = 3.79*10-6 C

q1 = 6.88*10^-6

answer: (a) the negative charge = -3.09*10-6 C; (b) the positive charge = 6.88*10-6 C

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