Balancing Charges on Identical Spheres

[Tridius]

Homework Statement

Two identical small metal spheres initially carry charges q_1 and q_2. When they're x=1.0m apart, they experience a 2.5N attractive force. Then they're brought together so charge moves from one to the other until they have the same net charge. They're again placed x=1.0m apart, and now they repel with a 2.5N force.

Homework Equations

F=kq1q2/r^2

The Attempt at a Solution

Alright, so this question seemed pretty easy but my answer isn't making any sense. First I solved for the net charge on the spheres after they had discharged,

F=kq3^2/r^2 ... q3=sqrt(Fr^2/k) = 1.667*10^-5C

Next I assumed that since the two spheres had balanced their charges, the original charges were 1.667*10^-5 +/- x.

Putting this back into the Coulomb's Law equation I got

F=k(1.667*10^-5 - x)(1.667*10^-5 + x)/r^2

But when I solved for x and then tried to sub it back into q1=(1.667*10^-5 - x) and q2=(1.667*10^-5 + x), both q1 and q2 were positive, which would not result in an attractive force.

Help please. =)

 

[rl.bhat]

Hi Tridius. welcome to PF.
In the first case, F = k*q1*q2/d^2.
In the second case, charge on each sphere is (q1 - q2)/2
So F= k*(q1 - q2)^2/d^2
Can you proceed now?

 

[Tridius]

Thanks a lot, this should really help. What I don't understand though is that if the charges are now (q1-q2)/2, then why is the force k(q1-q2)^2/d^2? Where did the 2 in the denominator go?

 

[rl.bhat]

Thanks a lot, this should really help. What I don't understand though is that if the charges are now (q1-q2)/2, then why is the force k(q1-q2)^2/d^2? Where did the 2 in the denominator go?

The force should be
F = k(q1-q2)^2/4*d^2

 

[Delphi51]

I don't understand why each charge is (q1-q2)/2.
If it was, then the total charge would be 2*(q1-q2)/2 = q1-q2.
But we know the total charge is q1 + q2.
Looks like the charge on each must be (q1 + q2)/2.

 

[rl.bhat]

I don't understand why each charge is (q1-q2)/2.
If it was, then the total charge would be 2*(q1-q2)/2 = q1-q2.
But we know the total charge is q1 + q2.
Looks like the charge on each must be (q1 + q2)/2.

Since the force is attractive, the charges must be of opposite nature.