# Can Magnetic Force Do Work?

1. May 10, 2013

### IGFSoft

I am revisiting a topic discussed in earlier threads, because I feel the answers given there are either incomprehensible or mistaken (or both).

It is well known that the force generated by a magnetic field acting on a moving charged particle is perpendicular to the particle's motion, and that it therefore cannot "do work" on the particle. That is, it can change the particle's direction, but not its kinetic energy. The question, then, is something along the lines of "How can electromagnets pick up cars?", the implication being that the car is clearly increasing its potential energy when it moves toward the magnet.

The proposed answers take several forms. Some think the question is related to conservation of energy, and point out that the energy really comes from the generator, or the power company. This misses the point. Some vanish into thickets of mathematical obscurity. Many seem to feel that the "answer" is so complicated that it is foolhardy to pursue it, or else that a detailed answer must lie in the realm of quantum mechanics or special relativity. Finally, it is frequently stated that there must be electric fields operating to lift the car, since the magnetic field cannot. The question of where exactly these electric fields come from trails off into the "too hard" response.

I think a large part of the confusion arises because the discussion overlooks a crucial aspect of the situation. Specifically, if you look at the behavior of, say, a nail, being picked up by a permanent magnet, you can say that the nail moves so as to increase the flux density passing through it. Which is to say, it goes where the lines of magnetic force are closer together. Since those lines radiate outward from the poles of the magnet, any reasonably compact geometry will ensure that the nail moves towards the magnet. But this requires that the magnetic field be diverging, and therefore, that there is no direction which is "the direction of the magnetic field". If it were somehow possible to make a magnetic field which did not diverge in some region of space (as I suppose it may well be), a nail placed in the region would not move toward the magnet.

2. May 10, 2013

### 256bits

Is the answer that magnetic lines of force being loops also try to become as short as possible, and in a magnetic field an iron nail becomes a magnet itself with N-S poles.

3. May 10, 2013

### lxgoodies

Ok my two cents on this.. now suppose it moves, accelerates. During that time, the field is loosing energy, because a metal object moves in to the (virtual) center of it, shortcutting field lines. Now this energy is not lost, it moves the object, add kinetic energy to it, accelerating it, even lifts its mass, against the force of gravity. That is the work the field performs.

Last edited: May 10, 2013
4. May 11, 2013

### Jano L.

I think you stated the problem quite well. There are two ways to answer it.

One is to introduce fundamental magnetic poles and forces between them; the force on a magnetic pole would be

$$\mathbf F = q_m \mathbf H.$$
where $q_m$ is magnetic pole. There are some books based on this, I think by Chu and Haus. It explains magnetic force between magnets easily, but nevertheless it is less popular view, because the magnetic fields are usually explained as due to microscopic electric currents and no microscopic magnetic poles were found.

In the second view, the work done on the nail cannot be done by the magnetic forces of the magnet, since these are always perpendicular to the velocities of the composing particles. It has to be another kind of force.

Two other important kinds of force in macroscopic theory are electric force and the force of constraint; the latter forces keep the charges within the metallic body and make it possible that the energy of the body and the energy of the currents can mutually interchange. It may be that these constraint forces are eventually also just electromagnetic forces on the microscopic level, otherwise invisible on the macrolevel due to their strong spatial variation on short distances.

The electric and the constraint forces can do work on the body. So one possible explanation is that when the magnet is approached towards the nail, the magnetic field changes the microscopic motion of the charges within the nail and this in turn changes the internal electric and constraint forces on the macrolevel. If the nail moves, it is due to the action of these forces upon the nail itself.

The attractive effect of the magnet is thus indirect, the actual working force originating in the nail itself. This may seem strange, but in electromagnetism it is possible, since the sum of internal forces does not need to be zero, due to relativity (electromagnetic forces do not obey the principle of action and reaction).

5. May 12, 2013

### universal_101

If the internal forces of the nail are non-zero and of course towards the magnet, then why does the magnet itself gets pulled towards the nail ? Does it also has non-zero internal forces in the direction of the nail ?

6. May 12, 2013

### Jano L.

I think so; the nail becomes magnet too, and its magnetic field changes the magnet etc.