Two identical conducting spheres, fixed in place, attract eachother with a force

Question

Two identical conducting spheres, fixed in place, attract eachother with a force of 0.115 N when their center to centerseparation is 45.00 cm. The spheres are then connected by a thinconducting wire. When the wire is removed, the spheres have a netpositive charge and repel each other with an electrostatic force of0.027 N. What was the initial negative charge on one of thespheres, and what was the initial positive charge on theother?(Hint: Use charge conservation and solve for one of theinitial charges. You will end up with a quadratic equation. Thesolutions give you the positive and negative charges.)

Explanation / Answer

   Let the initial charges be +Q and -q.    So, the force of attraction = -KQq/r2= 0.115 N    Now, since they are identical they have sameradii and thus the same electric potential for the samecharge.    So, when they are connected the net charge willbe equally divided through flow of electrons.    So, final charge on each = (Q-q)/2    So, force of repulsion =K(Q-q)2/4r2 = 0.027 N    Here, K = 9*109 , r = 0.45 m    So, on solving for Q and q from the twoequations, Qq = 2.5875*10-12 Q-q = 1.558*10-6 C Q-q = 1.558*10-6 C Q =  3.345*10-6 C , -q = -1.787*10-6 C   

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