Why does a magnet do work on a flying nail?

[alyssmainwrg]

When a charged particle moves in a magnetic field, the magnetic field will not work. But when a nail flying over a permanent magnet is attracted by the magnet, the magnet does work on the nail. Can anybody explain why this is so?

 

[hutchphd]

It is the forces that hold the nail together that do the work. In order to attract the nail there must be a gradient in the field ( a pole face of the magnet). The moving charges in the nail will be feel different magnetic forces and the constraining forces will do work to maintain the nail's integrity. If the nail were loose charges they would dissociate.

 

[rude man]

When a charged particle moves in a magnetic field, the magnetic field will not work. But when a nail flying over a permanent magnet is attracted by the magnet, the magnet does work on the nail. Can anybody explain why this is so?

There is pressure (think "suction") applied to a high-$\mu$ object like a nail in and by a magnetic field situated in a low-$\mu$ region. This pressure is equal to the magnetic energy density everywhere along the nail, and is everywhere normal to the surface of the nail if $\mu_{air} << \mu_{magnet }$, and is directed towards the region of higher B. So since the B field is stronger closer to the magnet the net suction, ergo force, is in a direction to accelerate the nail towards the magnet.

By conservation of energy, the increase in the nail's kinetic energy equals the reduction of the magnetic field's energy as the distance, ergo volume, of the mag field is reduced as the nail moves towards the magnet.

A stationary charge does not see a force applied to it since its permeability is low. There are probably better explanations in quantum mechanics. In any case a charged particle does not see a force applied to it unless it's moving, and even then the force is orthogonal to the direction of motion so $dW = \bf F \cdot \bf ds =0$.

PS - sorry, laTex seemingly not working.