Can a magnetic field ever do work on a current carrying wire?

[Tony11235]

It is possible for the magnetic field to do work? I know it cannot do work on a moving charge, but what about...a current carrying wire? Is there any situation where work can be done by a magnetic field?

 

[El Hombre Invisible]

Funnily enough, I've not long finished reading Feynman's collection of letters 'Don't You Have Time To Think?' where he was asked the same thing by a high school teacher who had told his class that a magnetic force could do not work, then later showed a paper clip being attracted to a bar magnet. The example you mentioned, two wires carrying currents in the same direction attracting each other (or in opposite directions repelling each other) is another good one.

I think it comes down to a question of what is really doing work in such magnetic interactions. Unfortunately Feynman didn't go into many specifics in the magnet/paper-clip example, answering more with a "Don't ask" attitude.

But in the case of the moving wires, the electrons are curved towards one side of the wire (no work done on them - change in direction only). It is then purely electric interactions that cause the wires to move (as the electrons in that side of the wire repel each other).

 

[Tony11235]

So the act of a paper clip being lifted and eventually attached to a magnet is considered work? Was Feynman trying to say the magnetic field can do work?

 

[El Hombre Invisible]

So the act of a paper clip being lifted and eventually attached to a magnet is considered work? Was Feynman trying to say the magnetic field can do work?

No, I think he was trying to argue that to explain what is actually doing the work in each counter-example is just mind-numbingly complex and would result only in frustration for the student asking the questions. Like the two wires example, there is an explanation showing that it isn't the magnetic field that is doing the work - it is the electric field.

Another good counter example would be an electron moving through a magnetic field such that the force is applied downwards (so the electron moves upwards), doing work to raise the electron's gravitational potential. I would have no idea how to explain that one.

Maybe it does do work, I don't really know. Ha! I will dig out the letter tonight.

 

[Tony11235]

I was having an argument with my physics professor about this. And she just challenged me to find a situation where it does do work. I am just finding it hard to believe that it's impossible for the magnetic field to do work.

 

[dicerandom]

Well you can see that the magnetic field doesn't do work simply from the Lorentz force, the magnetic field requires a velocity to exert a force and then the force it exerts is always perpindicular to the direction of motion. That's a rather cheap way out though, in my opinion.

Keep in mind, however, that when you change refrence frames the magnetic and electric fields also change. If you have a frame in which the field is entirely magnetic you can then transform into a frame moving relative to the first in which the field is both magnetic and electric. Combine this effect with the fact that a magnetic field can instigate charge separation and thus create electric fields and, as El Hombre mentioned, you can very quickly get some amazingly complex situations in which there are multiple sources of magnetic and electric fields which are tugging every which way on a particle.

It's good that you question these statements, and there are likely some simple cases that you will be able to work out, such as the two wire example given, but there will also be situations that will simply be too complex to get a grip on. In the end I think it's best to be comfortable with the reasoning and mathematics behind the fields and their interactions with the particles, then you can trust the mathematics to tell you the truth.