Inductance of a Helmholtz Coil?

[Mark Becker]

Hello -

I have been asked to build a small Helmholtz coil with the intent
being a .01T (100 gauss) field that will be turned off in something
like 100 nanoseconds.

Not having much experience with magnetics, I did some reading and a
few web searches. I think my coil design will work (some doubts.. is
the coil radius to the mean of the inside and ouside radii or just to
the inside radii?). However, in order to determine component values
for the sudden shut-off, I need to know the inductance of a Helmholtz
coil pair.

My coil parameters:
Inside Radii: 3 cm
Current: 2.5A
Wire Size: 22 AWG
Turns: 133.

I have seen expressions approximating the inductance of a solenoid..
and could double it to deal with 2 series-connected coils. However, I
believe the mutual inductance term is large enough to foul up the
design.

The inductance will be bounded by that of the sum of two separated
solenoids and that of one large solenoid extending over the entire
region. This is pretty extreme given the above geometry.

Anyone out there with a better approximation? Please?

Regards,

Mark

P.S. Anti-spam measures in effect. Please remove the NOSPAM where
obvious. Or post to the group.

 

[Mark Becker]

A little while ago I wrote:

My coil parameters:
Inside Radii: 3 cm
Current: 2.5A
Wire Size: 22 AWG
Turns: 133.

I received a comment from a helpful net.denizen... knowing the
winding geometry would be a Good Thing.. and apologies for not
including this information in my original post.

Each coil was to be about 8 mm wide and about 3.3 centimeters from the
inside radius to the outside radius. The total diameter of this thing
is then (3.3 + 6 + 3.3) or about 12.6 centimeters.

Spacing between the two ..disks.. is 3 centimeters.

I was planning on using heavy build enameled wire, 22 AWG and had
worked up a function for producing diameters for both bare copper and
enameled wire.

-----

Here is a link to an expression for the on-axis B-field of a real
Helmholtz coil:

http://www.netdenizen.com/emagnet/helmholtz/realhelmholtz.htm

Some manipulation of the special case expression for when x = 0
(on-axis and dead-center of the coil pair) permitted me to get a
handle on the first part of the design.

I hope that expression is correct.. and if someone has a link or
reference to the derivation of that expression, that would be Muchly
Appreciated.

Regards,

Mark