Verifying Electrostatic Charges: Q and q

[czaitz]

I have attempted this problem twice and have one more chance before I get the "red ex" so I thought I'd check my thinking.

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.136 N when their center-to-center separation is 65.0 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 0.0477 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?

To find q I used Coulomb's equation, solving for q, which is the charge on the spheres after they touch. That was q= 1.497E-6 C.
Then I thought that F=k Q(Q+2q)/r^2 but that made for some hairy quadratic action trying to get Q and Q+2.
Plus they said my answers were wrong twice.

For this one I got Q = 1.05E-6 C and then the other (+) ball would be 6.11E-6 C.

Is my thinking anywhere in the ballpark? I'm not so sure on the second part.

 

[Tomsk]

You're on the right track, you use the second situation to find the total charge, then substitute into the first situation to get a quadratic for the two initial charges. The substitution should be q2=2q-q1. Then q1(2q-q1)=F*r^2/k, which should give you the two answers you need.

 

[czaitz]

Thanks, but can you clarify the substitution? I callled the unknown charges Q and Q + 2q because 2q is what one sphere had extra before it discharged to the other sphere.
I'm not sure what the qs are in your substitution...q2 is 2q minus q1? The new charges are q2 and q1?

 

[Tomsk]

The two initial charges are q1 and q2, which you want to find. q is the charge on each sphere after they have been connected, they are both q as they have the same radius. This you found, 1.497E-6 C. The total charge is 2q, which is equal to q1+q2, as charge is conserved. So you substitute q2=2q-q1 into Coulomb's law for the first situation, and find q1, then put that back into 2q-q1 to get q2.