Work/Energy and Parallel Current-Carrying Conductors (Conceptual Question)

[nautikal]

Homework Statement

Two parallel conductors carrying current in the same direction attract each other. If they are permitted to move toward each other, the forces of attraction do work. Where does the energy come from? Does this contradict the assertion in the previous chapter that magnetic forces on moving charges do no work? Explain.

Homework Equations

Right-hand rule.

Magnetic potential energy:
$$U = -\vec{\mu}\times\vec{B}$$

$$\vec{\mu} = I\vec{A}$$

The Attempt at a Solution

I understand how they attract each other, but not where the energy comes from. Before the wires move together, there is just electrical energy in the wires. Afterwards the two wires are together, and they have negative magnetic potential energy relative to the beginning. Does this mean that the magnetic potential energy turns into electrical potential energy of the wires? The only explanation I can really think of is that the work done by the two forces somehow cancels out. Could someone please explain this problem, because I'm getting more confused the more I think about it :).

 

[Badi]

Faraday's law states that a changing magnetic field induces an electric field. So, the moment the current is allowed to pass in the two wires, a magnetic field is created in a region where there was none previously. This change induces an electric field which is responsible for the work done on and by the wires.
So magnetic forces still do no work.
(Check out Griffiths' Introduction to Electrodynamics chapter 7 for a nice explanation)