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 0.155 N when their center-to-center separation is 63.2 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 0.0408 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

Normally the distance between the center of the spheres is considered much greater than the radius so the charge movement within the spheres is neglected.

Considering the initial charges q1 and q2, and the respective charges q3 and q4 after the spheres were connected. You've found that q1q2 = -7.02 x10^-12 C^2 (negative since it's an attraction force of -0.158N) and that q3 = q4 = 1.196x10^-6 C.

From the conservation of charge, you can determine that q1 + q2 = q3 + q4.

So we've got 2 equations, 2 unknown variables:
q1 + q2 = 2.39 x 10^-6 C and
q1q2 = -7.02 x 10^-12 C^2

Solving this, you will get a quadratic equation looking like:
q1^2 - 2.39 x 10^-6 - 7.02 x 10^-12 = 0

for which the roots are the values of q1 and q2.

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