On Mar 8, 2008, at 4:05 PM, Robin van Spaandonk wrote:
In reply to Horace Heffner's message of Sat, 8 Mar 2008 15:15:02
-0900:
Hi Horace,
[snip]
Since you are talking about single layer tori, they
both have major axis hoop currents, and thus the confined fields of
both tori are shared with, overlap, the hoop fields of the opposed
tori, and thus there is a much stronger interaction than one would
obtain from the major hoop currents alone. I hope this is making
sense and is not just a lot of word salad.
[snip]
It makes sense to me, though if the major axis is common to both
tori, then the
extending field of the "first" torus would be largely perpendicular
to the
enclosed field of the other torus. In such a situation, would you
still expect a
strong interaction, and could you quantify it?
It sounds like you are assuming the two tori major axis planes are
parallel as well, both normal to the axis. If the radii are small in
comparison to the distance between the tori, and the major axes
planes are parallel and normal to the axis, and there is no high mu
material involved, then the force just boils down to the force
between hoop coils at that distance. If mu1 and mu2 are the hoop
coil magnetic moments, and d the separation between axis centers,
then the force is:
F = =3*mu0*mu1*mu2/(2*Pi*d^4)
If there is no magnetic core material, i1 and i1 the currents, r1 and
r2 the major radii, then
mu1 = pi*i1*(r1)^2
mu2 = pi*i2*(r2)^2
Torque depends on angle to the axis and is proportional to the 1/d^3
dipole field strength of the hoop current.
Again, this all assumes d is large in relation to r1 and r2. As
things get closer they change significantly, and the best way to
handle force and torque calculations is probably finite element
analysis.
What is your application? What are the dimensions involved? Are you
dealing with actual toroid coils, or merely using them as mental
models for orbitals or other physical realities?
Horace Heffner
http://www.mtaonline.net/~hheffner/
