Electric force and free electrons

[chem1]

Two point charges of -1.0 micro C and +1.0 micro C are fixed at opposite ends of a meterstick. Where could a) a free electron and b) a free proton be in electrostatic equilibrium?

I'm guessing the answer is nowhere since there have to be opposite charges to be in equilibrium?

 

[Dick]

I think you are right. The forces don't balance anywhere.

 

[chem1]

is there any way I can prove it with the formula kq1q2/r^2?

 

[Dick]

Put one charge at r=(1/2) and another at r=(-1/2). Then the magnitude (ignoring direction) of the force on the third charge located at x due to one charge is k/(x-1/2)^2 and the other is k/(x+1/2)^2. If you set those equal you find the only possible position is x=0. But at x=0 you know the directions of both forces are the same. So they can't cancel.

 

[chem1]

yes! that's what I thought... thank you!