Electrostatic force of Repulsion

[popo902]

Homework Statement

Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (Fig. 21-22a). The magnitude of the electrostatic force acting on sphere 2 due to sphere 1 is F = 6.5 N. Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (Fig. 21-22b), then to sphere 2 (Fig. 21-22c), and finally removed (Fig. 21-22d). What is the magnitude of the electrostatic force F' that now acts on sphere 2?

Homework Equations

F = (Q1*Q2)K/r^2

The Attempt at a Solution

so each touch takes away half the total charge in the beginning right?
first i thought it was half taken away from each sphere
so the final would be Q1 = Q1/ 2 and Q2 = Q2/2 and since theyre the same
i just combined them and made it Q1 *Q2 = Q/4
k is constant
r^2 is constant
so i though the answer would be 6.5/ 4
...but it's not
am i thinking the right way? what am i doing wrong?

 

[Doc Al]

When the conducting spheres touch, charges rearrange so that each sphere ends up with half the total charge.

If the original charge on the first two spheres is Q:

What's the charge on sphere 1 and sphere 3 after they touch?

What's the charge on sphere 2 and sphere 3 just before they touch?
What's the charge on sphere 2 and sphere 3 after they touch?

 

[popo902]

When the conducting spheres touch, charges rearrange so that each sphere ends up with half the total charge.

If the original charge on the first two spheres is Q:

What's the charge on sphere 1 and sphere 3 after they touch?

What's the charge on sphere 2 and sphere 3 just before they touch?
What's the charge on sphere 2 and sphere 3 after they touch?

so if each sphere has charge Q
so then charge on 1 would be 1/2 Q
the charge on 3 would be 1/2Q as well since it was neutral and got charged
then 2 would still be 1Q becasue it was not touched yet and 3 would still be 1/2Q
then after they touch 2 and 3 charges would add up to 3/2Q
then each would take away half from that?
so then 3/4 Q qould be the final charge for 2 &3
is that the right way of thinking?

 

[Doc Al]

Exactly.

 

[popo902]

Thank You!