Inductance of a Helmholtz coil pair?

[Mark Becker]

Hello * -

I have found a number of web sites that detail both theoretical and
practical treatments of Helmholtz coil pairs. Some deal with the
subject in excruciating detail, most show curves detailing
calculations or measurements of the vector B-field within the coil
pair.

I am trying to calculate the inductance of a Helmholtz coil pair.

It seems this should be treated as a pair of air-coupled coils.. which
means the mutual inductance needs to be calculated. I have an
expression for the inductance of a multi-layer multi-turn solenoid..
but the expression for the mutual inductance eludes me.

Suggestions, guidance, and/or pointers to sources of information would
be appreciated.

Regards,

Mark Becker