# Energy to separate charge +e and -e

1. May 13, 2013

### Saxby

1. The problem statement, all variables and given/known data
Derive an expression for the energy required to separate to infinity an electric charge +e and a charge -e, their initial separation being d.

2. Relevant equations

F = (q1*q2)/(4∏ * ε0 * d2)

3. 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 :)

2. May 13, 2013

### 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.

3. May 13, 2013

### ap123

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