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Q:
In our high school physics, we learn that magnetic force does not do work. But why do bar magnet stick together.
Our hands feel force and they really move in that direction.
It seems that some sort of work is done.
- PChan (age 22)
HK
A:
I love this question, partly because a few years ago my distinguished friend and colleague Sid Nagel and I spent a few hours discussing it, with no thought that there would ever be a chance to more or less publish the discussion.Let's break up the answer into two parts: the (easy) quantum case and the (subtle) classical case.First, particles such as electrons, protons, and even neutrons are themselves tiny magnets, each with a fixed magnitude of magnetic moment. There's a term in the energy proportional to μ.B, the dot product of the magnetic moment and the field. That term depends on position, since B depends on position. So it acts just like any other potential energy term, and is responsible for work. In other words, if you drop an intrinsically magnetic particle into a field, the field definitely does work on it. Since a lot of the magnetism in ordinary permanent magnets comes from this intrinsic spin magnetism of the electrons, there's a lot of plain ordinary work done by magnetism as two magnets pull or push on each other. To that extent, your school taught you wrong.
Second, though, they did have a reason to say what they said. If you look at a classical charged particle (no intrinsic magnetism) moving in a magnetic field, the field does no work on it. You know that because the force is proportional to vXB, where v is the particle velocity. That vector cross product is always at right angles to v, so F.v=0, i.e. no work is done on the particle.
OK, so here's where it gets interesting. We know that you can have a magnetic moment from an ordinary current going around a loop, and it can get pulled into a magnetic field just the way some permanent magnet would. Work gets done on it. Isn't it done by the magnetic field? And didn't we just show that couldn't happen?
I should put some drawings in here, and will try to do so later, but meanwhile here's words. Say that the magnetic field (from whatever source) is pointing mostly in the z direction, but getting weaker with increasing z, i.e. spreading out radially in the xy plane. This is just the standard picture of the field from a solenoid or cylindrical bar magnet aligned with the z axis. You've got a ring of conductor symmetrically arranged round the z axis with electronic current running around the loop. Let's say that it's a very good conductor, so the current isn't just running down over the time we're interested in, but not a superconductor so we can temporarily not worry about quantum effects.
Let's say that the direction of the current is such that the loop is pulled into the stronger part of the field. The reason that the field along z can get stronger near the source is precisely that the field is spreading out in the xy plane. So there's a little radial field. Take the cross product with the tangential electron velocity and you get a force in the negative z direction on all the electron current. That's at right angles to the current, so there's still no work done. But the electrons can't leave the wire. They bounce off the bottom (low-z) side, imparting momentum to the wire, i.e. exerting force on the wire. As soon as the wire starts to move, that force (in the -z direction) is along the motion of the wire, so it's doing work. The electrons are doing work on the wire, by whatever (non-magnetic) force causes them to bounce off the surface of the wire and stay inside.
What happens to the electrons' energy? They are now all moving, on average, in the -z direction, with the wire. That drives a magnetic force on them (again from the radial part of B) that slows down the tangential current. Energy is flowing from the moving electrons into the overall motion of the wire. The magnetic field causes that without actually doing any work.
Mike W.
(published on 05/18/2011)
Follow-Up #1: Can magnetic fields do work?
Q:
Can magnetic field/force do work on a current carrying loop? maybe it could possibly do work but INDIRECTLY? Or the main cause of work is the magnetic force/field on a loop because it deflects the charge? It makes no sense to me how magnetic fields/force do no work on a loop of wire carrying-current that resemble's a motor but more simplified...
I know as a fact magnetic fields/forces do NO WORK on a charged particle...
But a particle in motion through a conductor creates a electric dipole, thus the B field could possibly do work?
Thanks!
- Miyze (age 20)
Colorado
A:
As it happens, we've answered just this question before, but it may have been hard to find. So I've marked it as a follow-up.
Mike W.
(published on 08/06/12)
Follow-Up #2: more magnetic work
Q:
I'm sorry but I didn't understand your answer. could you explain it more perspicuous. thanks
and something else:
when a magnetic crane lifts the carcass of a junked car,what is doing work?
- ali (age 20)
Iran
A:
Here's a shorter summary of the argument.
1. For most magnetic materials, including iron, the magnetism largely comes from electron spins which are magnetic themselves, not from electrical currents. The usual saying about magnetic fields not doing work is simply false in this case.
2. When all the magnetism comes from currents, the magnetic field does no work. However, by steering the electrons in new directions it can cause them to bounce off things and do work. So the magnetic field causes work but doesn't do it itself. Think of it as being sort of like a boss.
With regard to the crane, work is done at many points where mechanical energy is transmitted from one part of the machine to another. Probably you're asking about the actual magnet and the car. The car is made of steel, with magnetism coming from aligned electron spins. The magnet simply does work on it, as in our point (1).
Mike W.
(published on 12/26/12)
Follow-up on this answer.
