Re: magnetic fields

["John S. Denker" <jsd@MONMOUTH.COM>]

At 08:36 AM 9/6/01 +0200, Savinainen Antti wrote:

> 1) Why there is no magnetic potential and magnetic potential energy
> associated with magnetic field? Or is there?

There is.

Energy density proportional to the square of the field strength.

> 2) It is clear that magnetic field cannot do work on a moving charged
> particle.

OK.

> But in case of a bar magnet magnetic field seems to do work: it can attract a
> piece of iron and displace it. What energy transformation is associated with
> this? What changes, if any, take place in the bar magnet and its magnetic
> field? To put it shortly: who pays the bill?

Whoever magnetized your magnet paid the bill.

The easy way to think about it is in terms of magnetostatic field energy
per unit volume.  (There are close analogies to electrostatic field energy
per unit volume.)

To demonstrate, consider the force with which a small ball of iron is
attracted into a region of high magnetic field.  To a first approximation,
the field has energy density proportional to the square of the field
strength everywhere EXCEPT inside the iron.  If the iron is small enough so
that you can treat it as a "test particle", i.e. so that it doesn't
horribly short out the field pattern you are trying to observe, then you
can calculate the force on the iron by the principle of virtual work, based
on the magnetic field energy it "displaces".

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Big hint:  Feynman volume II chapter 8 and chapter 27.