# Work done moving two charges together

1. Feb 1, 2012

### phosgene

1. The problem statement, all variables and given/known data

Two point charges of magnitude +10 μC each are placed 0.2 m away from each other.

a) How much work is done in placing the second charge?

b) Is there any point at which the electric field and electric potential are both 0?

2. Relevant equations

Work = (charge of first point charge)(ΔV of second charge)

E=kQ/(d^2), where E = electric field, k = proportionality constant, Q = charge of point charge, d = distance from point charge

V=kQ/r, where V = voltage, Q = charge and r = distance from charge

V=Ed, where V = voltage, E = electric field and d = distance from point charge

3. The attempt at a solution

a) I assumed that the point charge was being moved from a spot far enough so that it could be approximated by being moved there from an effectively infinite distance away. Then the work done can be determined as follows:

Work = 10 μC(kQ/r2 - kQ/r1), where r2 = 0.2m and r1 = infinity

These simplifies to Work = (10 μC)(k10μC)/0.2m

b) I said that at a point very far away the electric field and electric potential will be 0. This is because E=kQ/(r^2) at a very far away point will effectively be E=kQ/(infinity), which is approximately 0. As the potential difference is equal to the electric field multiplied by the distance, it too will effectively be 0 at that same far away point.

Is my reasoning correct?? I don't really get voltage, potential difference and electrical potential energy.

EDIT: Sorry! I forgot to put a title! It should be 'Work done moving two charges together and possible point of zero electric field and electric potential'. But I can't edit a title in.

2. Feb 1, 2012

### tiny-tim

hi phosgene!
ok (but you need it in joules)
i'm not sure that we can talk about a point actually being at infinity

perhaps it would be easier to make use of the fact that both the potential (as a scalar) and the field (as a vector) are additive?

3. Feb 2, 2012

### phosgene

Thanks for the reply. I don't quite understand what you mean:(. But I think I have a better answer for b). The point exactly in-between the charges has an electric field of zero because the electric field vectors from both charges are exactly equal and opposite. The electric potential at this point is also zero because if a test charge is placed there, it will not move because the forces on it are equal.

4. Feb 2, 2012

### tiny-tim

hi phosgene!
no …

zero potential means that it is at the same potential as at infinity

(ie that no net work would be done moving it there from infinity)

compare this with a ball at the top of a mountain …

it won't move, but its gravitational potential is a lot more than at the bottom of the mountain

(ie a lot of work would be done moving it there)

oh, and you can just add potentials​