How do I calculate the force between a charged and a neutral sphere

[QaH]

Homework Statement

Two otherwise identical, small conducting spheres have charges +6.0 µC and −2.0 µC. When placed a distance r apart, each experiences an attractive force of 9.1 N. The spheres are then touched together and moved back to a distance r apart. Find the magnitude of the new force on each sphere.

Homework Equations

F_e=kq₁q₂/r²

The Attempt at a Solution

The first thing I did was solve for r, r=√kq₁q₂/F_e=√8.98755×10⁹×6×10^-6×2×10^-6/9.1N=0.1089meters
after the spheres come together there final charges will be +4μC and 0μC
I don't know where to go from here because when you plug a 0 charge into coulombs law you get 0 force.

 

[gneill]

after the spheres come together there final charges will be +4μC and 0μC

Are you sure about that?

 

[QaH]

Are you sure about that?

No, but I assumed the positively charged sphere will gain electrons when touched with the negatively charged sphere. An amount equal to -2 μC
6q-2q=4q the negatively charged sphere will have lost electrons equal to -2μC, -2q-(-2q)=0

 

[haruspex]

No, but I assumed the positively charged sphere will gain electrons when touched with the negatively charged sphere. An amount equal to -2 μC
6q-2q=4q the negatively charged sphere will have lost electrons equal to -2μC, -2q-(-2q)=0

Think about potentials. What do you know about potential in different parts of the same conductor?

 

[QaH]

They are the same? So the final charge will be +2 and +2?

 

[haruspex]

They are the same? So the final charge will be +2 and +2?

Yes.