Two identical conducting spheres, fixed in place, attract each other with a forc

Question

Two identical conducting spheres, fixed in place, attract each other with a force of 0.093 N when their center to center separation is 59.00 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres have a net positive charge and repel each other with an electrostatic force of 0.041 N. What was the initial negative charge on one of the spheres, and what was the initial positive charge on the other?(Hint: Use charge conservation and solve for one of the initial charges. You will end up with a quadratic equation. The solutions give you the positive and negative charges.)

Explanation / Answer

note that after connecting the wire,

both must have equal charge

0.041 = k q^2 /(0.59)^2

q = [0.041*0.59^2/(9*10^9)]^1/2

q = 1.259 micro C

hence,

totAL charge =   1.259 micro C+ 1.259 micro C = 2.518

also,

0.093 = - k (q1* q2)/0.59^2

q2 = ( 2.518 micro columb - q1)

solving it,

q1* (2.518-q1) = - 3.59 7

q1 =3.535 micro columb

q2 = - 1.017 micro columb

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