On Mar 7, 2008, at 2:25 PM, Robin van Spaandonk wrote:
Hi,
If one has two separate toroidally wound inductors, and one passes
a DC current
through each coil, do they experience any force from one another,
particularly
when sharing a common major axis?
I'm interested in both theoretical and experimental responses.
It is typically assumed that, with the exception of leakage flux,
that all of the flux is held within the tori minor radii, thus there
is no interaction between current carrying tori when pure DC is
used. There indeed is always, both theoretically and experimentally,
small leakage fields from the windings, which can readily be detected
when AC current is used. However, when experimenting, it is very
easy to make a serious mistake in regard to the above, and which is
not related to leakage flux at all. That mistake is to not ensure
that an even number of winding layers is used for each torus, with
winding direction reversed at layer termination boundaries, so as to
avoid major axis net current loops. For example, if a single winding
layer comprised of 100 turns is used, then the torus winding is
equivalent to 100 ideal current hoops about the minor axis carrying
i, plus the equivalent of a single conductor hoop coil centered on
the major axis and having the major radius and carrying current i
(this is equivalent to a current hoop running through the center of
the "cake of the doughnut" carrying current i). If both tori have an
odd number of winding layers, or even if multiple winding layers are
used but all or most proceed in the same major axis direction, or
some combination of the above resulting in a net major axis current
hoop, then they both carry a significant external magnetic field
equivalent to hoop coils about their major axes. A pair of tori with
such equivalent hoop coils will exhibit significant mutual forces and/
or torques depending on location and orientation. Note that such
forces can be larger than just the force between the major axis hoop
currents, because flux from one hoop coil can enter the "cake of the
doughnut" volume of the adjacent torus, and thus interact with the
flux there (or be viewed as interacting with the small radius
windings) to produce much larger forces than might otherwise be
anticipated. This also means unexpected force interactions can arise
between a major axis hoop current carrying torus and a torus not
having such a hoop equivalent current, including a permanent magnet
torus in which all flux is internal. Flux repels (or attracts)
parallel flux via magnetic pressure.
A very interesting and surprising experiment (for me anyway) was the
investigation of the vicinity of an iron core toroid coil by means of
an approximation to a magnetic monopole probe I made by taping
together a long (about 6" long) stack of 3/8" thick circular ceramic
magnets (3/4" dia. if I recall). When the toroid coil is driven by
AC current it is very easy to sense magnetic field strength manually
from the vibration of the probe when it is hand held (at least with
the coils I used, which were #10 or #12 wire carrying 20 amps or
so). By far, the strongest vibrations are obtained when a probe tip
is in the center of the torus. I put a little plywood platform in
the center of the torus and placed a single disc ceramic magnet
there. It danced about in a lively fashion and slowly rotated as well.
A much better approximation to a monopole probe could be made using
smaller diameter magnets joined into a longer probe. This probe
technique seemed much more sensitive, but provided similar results to
a FET probe I made, with regard to determining field envelope shape.
The FET probe required AC, but the simple monopole approximating
magnetic probe should work with DC.
Horace Heffner
http://www.mtaonline.net/~hheffner/
