Re: Bar magnets, was magnetic circuits

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

At 11:05 PM 2/18/01 -0500, Ludwik Kowalski wrote:

> > That's not a good way to think about it.
>
> Why did you say so?

Because it is really, really, not a good way to think about it.

I was trying to be polite by not focusing on the wrong ideas, hoping the
wrong ideas would quietly wither away and be replaced by correct scaling
laws, correct analogies to electrostatics, and useful techniques like
magnetic circuit analysis (magnetomotive force and all that).

>  It is true that this kind of thinking does not
> lead to a quantitative solution.

We agree, it is not quantitatively correct.

> But it is a good simple model for qualitative reasoning.

No.  It is not even qualitatively correct.
It is wrong physics.  It makes qualitatively wrong predictions.

> I suppose that an electrical engineer would
> be able to calculate the force between the coaxial poles of two
> bar magnets separated by a gap of any length.

Yes.  For simple geometries, it is an easy calculation.

> But I do not know how to use such information in order to
> predict, for example, that the attractive F is about 0.5 N when
> the air gap is 3 mm.

I outlined the calculation in my previous note.  Also, a search such as
  http://www.google.com/search?q=magnetic+circuit+OR+circuits+reluctance
will turn up lots more details including worked examples.

> Is it not true that the simple model I used is better than
> nothing?

Alas, it is worse than nothing.

Over 350 years ago there appeared a book called "Discourses on Two New
Sciences".  One of the new sciences was the laws of motion.  What was the
other one?  Scaling laws!

I think scaling laws are very important.  The field of a point charge
scales like 1/r^2.  The field of a line charge scales like 1/r.  The field
of a surface charge scales like r^0.

Saying that there is some magical "1/r^2 law" that applies to everything is
just not right.  Certainly there is no 1/gap^2 law that applies to
parallel-plate capacitors.  Why should there be a 1/gap^2 law that
magically applies to the magnetic "charges" (poles) on the ends of bar magnets?

The idea that the end of the bar magnet has just a fixed density of
pole-strength makes so many wrong predictions that it is impossible to list
them all.  I hardly know where to begin.
 -- the scaling behavior is wrong.
 -- the directional behavior is wrong (consider the field off to one side).
 -- the behavior under reversal of one of the magnets is wrong.
 -- the behavior when one of the magnets is replaced by unmagnetized iron
    is wrong.
 -- the predicted inductance is wrong.  (Consider what you would see by
    wrapping wires around the components).
 -- et cetera......

> Even pure monopoles,
> interacting with the 1/r^2 force would behave in that way.

No, they wouldn't behave the same way.  Add that to the list of wrong
predictions.  That's why the wrong model is wrong:  it makes qualitatively
wrong predictions.