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)

 

[thomate1]

I can provide some insights into this question. First, let's clarify that the assertion in the previous chapter, that magnetic forces on moving charges do no work, refers to the force exerted on an individual charged particle in a magnetic field. In this case, the particle experiences a force, but it does not undergo any displacement, so no work is done.

However, in the case of two parallel current-carrying conductors, the situation is different. Here, the conductors themselves are moving towards each other, and thus undergoing a displacement. The attractive force between the conductors is due to the interaction of their magnetic fields, and this force does work on the conductors as they move towards each other.

So where does this energy come from? It comes from the electrical energy stored in the conductors. When the conductors are initially placed parallel to each other, they have a certain amount of electrical potential energy due to the charges and currents flowing through them. As they move towards each other, this potential energy is converted into kinetic energy, and finally into magnetic potential energy as the conductors come into contact.

In other words, the energy comes from the conversion of one form (electrical potential energy) to another (magnetic potential energy) as the conductors move towards each other. This does not contradict the previous assertion, as the work is being done on the conductors as a whole, not on individual charged particles.

I hope this explanation helps to clarify the concept of work and energy in this scenario. It is important to consider the system as a whole and the different forms of energy involved in order to fully understand the situation.