Chronology |
Current Month |
Current Thread |
Current Date |

[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |

*From*: "John S. Denker" <jsd@MONMOUTH.COM>*Date*: Sun, 18 Feb 2001 17:42:45 -0500

Jack Uretsky wrote:

> What makes you believe that the pole strengths of interacting

> bar magnets is independent of distance?

Then at 03:42 PM 2/18/01 -0500, Ludwik Kowalski wrote:

My high school textbook, I suppose. Thanks for a good hint.

Let me follow it? As one end of the bar magnet comes closer

to another it induces "poles of the opposite kind at the surface.

That's not a good way to think about it.

It is similar to what happens in many dielectric materials. The

net pole becomes stronger at each bar magnet and the attractive

force between them changes more rapidly with the distance

than the 1/r^2 law would suggest. That is why magnets come

toward each other suddenly.

What 1/r^2 law is that? The law for magnetic monopoles?

The corresponding 1/r^2 law for electric charges does not produce a 1/gap^2

force for capacitor plates at constant charge; in fact it produces a force

that goes like gap^0 (i.e. independent of gap) in that case.

So please, before we use analogies to explain facts, let's make sure the

facts are true, and draw analogies to things that really happen.

We are not trying to explain why the force goes faster than 1/gap^2; we

are trying to explain why it goes faster than gap^0.

If the bar magnet really did have constant pole strength on its end, the

force law would be a nonsingular (indeed exceedingly gentle) function of

gap, and there would be no trouble establishing equilibrium between the

magnet force and the spring force.

======================

The sensible way to think about this is as a magnetic circuit. Haul out

the usual formalism of flux, magnetomotive force, and reluctance. The EB

writeup is not too bad:

http://www.britannica.com/bcom/eb/article/printable/4/0,5722,51234,00.html

I don't know of a really good discussion of this, perhaps because it is a

somewhat flaky technique, but it would be nice to at least get a decent

discussion of the limits of validity. Somehow I prefer controlled

approximations to uncontrolled approximations.

Anyway, to simplify the calculation, rather than using bar magnets, let's

suppose we have a horseshoe magnet, and we are putting the keeper on

it. We measure the force as a function of the gap. In this case,

practically all of the reluctance is in the gap, the flux goes like 1/gap

(assuming constant MMF and using the magnetic equivalent of Ohm's law), the

field energy density goes like 1/gap^2, the extensive field energy goes

like 1/gap, and the force goes like -1/gap^2 by PVW (principle of virtual

work).

(I reiterate that electrically charged spheres have a force as a function

of gap that doesn't look anything like this.)

How come that Coulomb was able to determine the 1/r^2

dependence using a torsion spring balance?

I suppose he was clever enough to use sources that were small compared to

the gap between them.

I also suppose he was clever enough to use stiffer springs to measure the

larger forces.

I suppose he was dealing with repulsive forces only.

I strongly doubt he restricted himself to repulsive forces only.

- Prev by Date:
**Re: Bar magnets** - Next by Date:
**Re: Taste: Microwave Heating vs Boiling** - Previous by thread:
**Re: Rossetta Stones of Physics ( Black Holes)** - Next by thread:
**Pulleys (Spanish rig?)** - Index(es):