Electric PE of a system of point charges

[eurekameh]

My physics textbook defines the electric potential energy of a system to be equal to the external work that must be done to assemble the system, bringing each charge in from an infinite distance. And then it goes on the explain an example:

"Figure 24-15 shows two point charges q1 and q2, separated by a distance r. To
find the electric potential energy of this two-charge system, we must mentally build
the system, starting with both charges infinitely far away and at rest.When we bring
q1 in from infinity and put it in place, we do no work because no electrostatic force
acts on q1. However, when we next bring q2 in from infinity and put it in place, we
must do work because q1 exerts an electrostatic force on q2 during the move."

Now, my question is:
Why do we not do work when we bring q1 in from infinity? We are exerting a force over a distance, are we not? Why is it dependent on the presence of an electrostatic force / field?

 

[CompuChip]

We are only interested in the electromagnetical properties of the system.
Of course, if you had to go and take your tweezers, pick up the charge from a point far away (note that in a practical setup something like one meter would probably already count as "infinity") and bring it over you would have to do something.

I suppose you could wind up a spring at infinity, use it to catapult the particle over a frictionless surface, and stop it using another spring from which you can gain the original energy back if you relax it.The point is that there are no electrical forces at work.

So even in such a setup you would get less energy back from the "stopping" spring than you needed to put in in the first place

 

[rcgldr]

I don't like the way this was explained. You have some reference point with two objects an infinite distance away from each other and also the reference point. You move one of the object to the reference point, but since the other object is still an infinite distance away, "no work was done" when moving from one infinite distance to another infinite distance.

I would prefer to change the origin of the frame of reference to one of the points, in which case no work was done because no object was moved.

Also both q1 and q2 exert electrostatic forces on each other, but the figure is only considering the electrical field created by charge q1.

Coulomb's law shows the force between two charges:

http://en.wikipedia.org/wiki/Electrostatics#Coulomb.27s_law

Scroll down a bit and you'll see the defiinition of an electric field, which is the force per unit charge created by a charged object:

http://en.wikipedia.org/wiki/Electrostatics#The_electric_field

Electrical potential energy is related to the charge on each object and the distance between them:

http://en.wikipedia.org/wiki/Potential_energy#Electric_potential_energy