Inductance of a Helmholtz Coil?

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.

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:

formatting link

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