Re: magnetic monopoles

On Wed, 30 Aug 2005, Ken S. Tucker wrote:

> I start with a 2" que ball and drill in 1/4" dia
> holes a 1/2" deep, spaced a 1/2" apart and place
> into those holes cylindrical bar magnets with N
> pointed out. I could do the same using S pointed
> out.
>
> Irrespective of the orientation of those balls on
> a pool table the N's will repel the N's and the
> N's will attract the S's, but by the 1/r^3 rule.

This might leave you with 8 magnets around the equator, one at each of the
physical poles, and maybe 4 in each of the mid-latitudes.

I predict a field that falls off as 1/r^7 (at long distances, anyway)
since you'd have approximately a 2^5 pole source. (What would the
force between two 2^5 poles be, and how would it depend on the
orientation? Sounds like something best left for students ... )

With 1 magnet you have a dipole (a 2^1 pole), with 2 holes on opposite
sides with magnets, you'd have a linear quadrupole, a 2^2 pole, with a
1/r^3 potential, and therefore a 1/r^4 field.

A row around the equator gives you a 2^3 pole, with 1/r^4 potential, and
1/r^5 field.

The general formula being 2^n pole, with 1/r^(n+1) potential, and
1/r^(n+2) field, where n is the number of rows of magnets from pole to
pole, counting magnets at the poles as well. Each pair of rows you add
increases n by 2.

In the limit of the sphere become infinitely densely packed by skinny
magnets, n goes to infinity, and the external field vanishes.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
.

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