Geometry,k, and mode

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Original poster: "Jolyon Vater Cox by way of Terry Fritz <teslalist-at-qwest-dot-net>" <jolyon-at-vatercox.freeserve.co.uk>

Dear List,
Is there a calculation for k based purely on the geometry of the coil 
components irrespective of the number of turns
e.g. one that derive k from the dimensions of two concentric cylinders for 
two solenoids -or a cylinder and a disk with a hole in the middle for a 
solenoid plus flat spiral?
Also, how is the mode determined from k?
I would like to know more.