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Question

Two identical condncting spheres, fixed in space, attract each other with an electrostatic force of 0.108 N when separated by 50.0 cm, center-to-center. A thin conducting wire then connects the spheres, When the wire is removed, the spheres repel each other with an electrostatic force of 0.0360 N. What were the initial charges on the spheres?

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Solution

initial charges = q1andq2
Force of attraction = 0.108N=14πϵq1q20.52
charges after the connection is made and removed = (q1q2)2and(q1q2)2
Force of repulsion = 0.036N=14πϵ(q1q2)24×0.52
therefore,
q1q2=3.0012×1012 and (q1q2)2=4×1012
q1=q2=1μF

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