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

[John Denker <jsd@av8n.com>]

On 05/14/2008 01:08 PM, Jeffrey Schnick wrote:

> I address the force question for the case in which the separation of the
> magnets is so great that you can treat them as point particles, each of
> which has a magnetic dipole moment, in chapter 17 of Calculus-Based
> Physics II at:
> http://www.anselm.edu/internet/physics/cbphysics/downloadsII.html .
> That discussion uses an equation from chapter 15.

I suppose that's useful, in a crawl-before-you-walk sort of way, but 
it doesn't directly respond to the original question, which involved
building a motor.  The "distant dipole" approximation is nowhere
valid in a well-designed motor.

Perhaps a more directly useful approach is the idea of energy in the
field lines, with energy density proportional to B^2, i.e. total energy
proportional to the integral of B^2 d(volume).  This energy is connected
to the force via PVW (Principle of Virtual Work) in the usual way.  This
gets used a lot, because it is super-easy to calculate or at least estimate,
even if the objects are not distant and/or not dipoles.  (Also, the same idea
works great for dielectrics in an electric field.)

For example, it is a fun exercise to show that in the far-field limit,
the force on a chunk of iron in the field of a bar magnet or solenoid
goes like 1/r^7.  The exponent is not what most kids would have guessed,
butit is easy to understand in terms of the physics.  (Again, far-field
behavior is not directly relevant to motors ... but the B^2 dV idea is.)