Electric charge problems

1. The problem statement, all variables and given/known data
Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.108 N when their center-to-center separation is 50.0 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 0.0360 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?

2. Relevant equations


3. The attempt at a solution

What I did was plug and chug
same for the second one F2=.0360 etc.. But I got it wrong.
I can not understand why for the second equation it has to be F2=k((q1+q2)(^2)/4r^2). From what I think, since the charge is conserved, shouldn’t it be the same as the original equation? Or am I misinterpreting the book or something? I just cant figure out why Fa=kq1q2/r^2 but Fb=k((q1+q2)(^2)/4r^2) or where did the (q1+q2)/2 came from? Thanks in advance.
Sorry, I am so slow with these things.


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