Energy to separate charge +e and -e

[Saxby]

Homework Statement

Derive an expression for the energy required to separate to infinity an electric charge +e and a charge -e, their initial separation being d.

Homework Equations

F = (q₁*q₂)/(4∏ * ε₀ * d²)

The Attempt at a Solution

Basically what I've done is first make q₁= +e and q₂= -e and substituted them into the equation above. I then integrated this equation as show below...

Work done = ^∞∫_d F = ^∞∫_d -e² / (4∏ * ε₀ * d²)

After integrating this with respect to d, I get the answer...

W = e² / (4∏ * ε₀ * d)

Is this correct or did i make it all up in my head, thanks for any replies :)

 

[barryj]

I think this is correct. The potential of a charge, v = kq/r , is found this way, i.e. by integrating from d to infinity of a test charge and then dividing by the charge.

 

[ap123]

An easier way to do this is to work out the change in potential energy.
W = ΔU