Re: [Phys-l] magnetic forces & potential energy

[John Denker <jsd@av8n.com>]

On 05/14/2008 08:54 AM, Paul Lulai wrote:

> The student has magnets that state they have a 'strength' of 200 pounds.
> I believe that this is the force of attraction btn the magnet and a
> ferromagnetic substance when the two are in contact.  Is there a high
> school method (algebra or calc 1 method) that would make it possible to
> calculate:
> 1- the force of attraction btn two magnets (one electromagnet & one
> permanent magnet) when they are separated by some distance?
> 2- the potential energy of a two magnet system in which the two magnets
> are separated?
>
> Your help is appreciated.  I haven't used much of my e&m since I took
> the course.  It appears I've forgotten quite a bit.  A bit shameful.  

I'm not convinced you "forgot" this.  You could easily get a physics PhD 
from a big-name school without ever seeing this covered in class.

If you just want something that works at the "gee whiz" level, you can 
get the job done using "magnetic circuit" ideas.
  http://www.google.com/search?q=magnetic-circuit+reluctance

We have the idea of a "magnetic circuit" (in analogy to electric circuit) 
with some "reluctance" (in analogy to resistance).

If you want the next level of detail ....... 

The analogy between magnetostatics and DC circuits is very imperfect.  It 
will give you the lay of the land, in general terms, but it usually does
not give precise results for practical structures.

You can see where the problems begin by considering the fact that the 
permeability of (say) iron is not infinite compared to the permeability
of air or vacuum.  This stands in unpleasant contrast to electrostatics,
where we usually take the resistivity of air (and other "insulating"
materials) to be infinite.

The situation is further complicated by nonlinearity;  the slope of the 
B versus H curve for a ferromagnetic material is huge near B=0 but 
drops to near unity in the saturated regime.

The moving parts in a motor or solenoid mean you have not just one
configuration to consider, but many.

It is definitely possible to design solenoids and motors using only
"magnetic circuit" ideas ... but is a tremendous amount of work.  My
father did some of this as part of his job, without benefit of 
computers.

Nowadays everybody uses FEM (finite element modeling).  Actually the
sensible approach is to use magnetic-circuit ideas to get you into
the ballpark, then use FEM to understand what you've got, then use
magnetic-circuit ideas to motivate some refinements, then use FEM
to look at the new structure, and so forth, iteration by iteration.

Pointers to a few modeling programs can be found via:
  http://archive.chipcenter.com/circuitcellar/january01/c0101rp62.htm
  http://www.google.com/search?q=magnetic+simulator

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

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