Electrostatic force sphere problem

[jssutton11]

The problem: Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.158 N when their center-to-center separation is 63.2 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 0.0322 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge in coulombs on one of them and (b) the positive charge in coulombs on the other?

So first I found the charges of the two spheres after the wire had been removed, since I knew that the charges must be equal. They both have a positive 1.196x10^-6 C charge. Now I am stuck trying to figure out the initial charges. Can anyone help me out? I used the Coloumbs Law equation F=(k|q1*q2|)/r^2 to find out what both charges multiply out to initially, which should be 7.02x10^-12 C. I have no idea where to go from there though.

 

[Defennder]

I'm puzzled by this question. Since this is a conducting sphere, the charges are free to move and when they attract each other initially they'll move to the region on the sphere which is closest to the other sphere. You're given the centre-centre separation distance but not the radius of the sphere. The same consideration occurs when they are repelling each other.

 

[l'ingenieur]

Normally the distance between the center of the spheres is considered much greater than the radius so the charge movement within the spheres is neglected.

Considering the initial charges q1 and q2, and the respective charges q3 and q4 after the spheres were connected. You've found that q1q2 = -7.02 x10^-12 C^2 (negative since it's an attraction force of -0.158N) and that q3 = q4 = 1.196x10^-6 C.

From the conservation of charge, you can determine that q1 + q2 = q3 + q4.

So we've got 2 equations, 2 unknown variables:
q1 + q2 = 2.39 x 10^-6 C and
q1q2 = -7.02 x 10^-12 C^2

Solving this, you will get a quadratic equation looking like:
q1^2 - 2.39 x 10^-6 - 7.02 x 10^-12 = 0

for which the roots are the values of q1 and q2.