Inductance of an arbitrarily shaped coil with varying turn density

[eastblue]

Dear all,

I would like to estimate the inductance of a rather arbitrarily shaped coil composed of multiple single loops. For example, I am wondering about the inductance of sandglass like coil which has many turns at the edge and less in the middle.

The inductance of a single loop seems to be well-known. How can I find out the inductance of a coil composed of these single loops? Would it be just a simple sum of them? Do I need to consider the mutual inductance between single loops as well?

Thank you in advance.

 

[marcusl]

You add self-inductances (assuming the coils are in series) and, yes, then take into account the mutual inductances between every pair of coils.