Parallel Wires and Magnetic Field

[kimberlyann9]

Homework Statement

Consider 2 parallel wires with currents running down them in the same direction. The first is fixed in place unable to move. The second is allowed to move. They exert an attractive magnetic force on one another, and the second wire moves towards the first. The second moves and speeds up; work is done. Magnetic fields do no work on moving charged particles. Is this statement violated in this situation?

Homework Equations

The Attempt at a Solution

Not really sure. It seems like the magnetic force would be enough to allow the 2nd wire to move, although the field itself does no work, the magnetic force can?

 

[Antiphon]

To solve this you have to really look hard at the forces. No work is done on the charges. But that doesn't mean no work is done on the wire.

Work is F.dl. The charges are moving perpendicular to the force, so that's zero. Is there anything that is moving along F?

 

[kimberlyann9]

To solve this you have to really look hard at the forces. No work is done on the charges. But that doesn't mean no work is done on the wire.

Work is F.dl. The charges are moving perpendicular to the force, so that's zero. Is there anything that is moving along F?

I'm so confused! So F and v are always perpendicular so that is why there cannot be any work done. F=ILB and there is current through the wire so does that have something to do with it?

 

[Antiphon]

Think of it like this; the charge is moving along the wire but the force is perpendicular to the wire. So the force pulling on the wire (sideways) can't be doing work on the charges along their direction of motion.

That doesn't mean that work isn't being done to accelerate the wire sideways- it is. But the sideways acceleration doesn't do work against the current, it does work against the mass of the wire to accelerate it sideways.

The work goes into moving the wire sideways, not pushing or pulling on the charges along the direction of the wire.

 

[asteriatic]

I would say that the statement is partially violated in this situation. While it is true that magnetic fields do not do work on moving charged particles, the presence of a magnetic force can still result in work being done. In this case, the attractive magnetic force between the two parallel wires is causing the second wire to move towards the first, and work is being done as the second wire speeds up.

This can be explained by the fact that magnetic fields are created by moving charges, and the magnetic force between the wires is a result of the interaction between these moving charges. So even though the magnetic field itself does no work, the force it exerts on the moving wire allows for work to be done.

Furthermore, it is important to note that the work being done in this situation is not being done by the magnetic field, but rather by the mechanical energy of the moving wire. The magnetic field is simply facilitating the transfer of energy between the two wires.

In conclusion, while the statement may seem to be violated at first glance, a deeper understanding of the interaction between magnetic fields and moving charges reveals that it is not entirely accurate in this situation.