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 0.159 N when their center-to-center separation is 63.5 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 0.0528 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

Let q1 be the first initial charge and q2 be the second one

after they are connected each has a charge q which = the difference of the first charges i.e. q1 - q2

so k*q1*q2/.5^2 = 0.159N or q1*q2 = .159*.635^2/9.0x10^9 = 7.12x10^-12

or q2 = 7.12x10^-12/q1

and after we have k*q^2/.635^2 = 0.0528
so q = sqrt(0.0528*.635^2/9.0x10^9) = 1.53x10^-6C

so q1 - q2 =1.53x10^-6

Now subbing in for q2 we get q1 -7.12x10^-12/q1 = 1.53x10^-6

rewriting

q1^2 - 1.53x10^-6*q1 - 7.12x10^-12 = 0

solving the quadratic eqn we get q1 = -2.01x10^-6 or 3.54x10^-6

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