How to estimate inductive coupling between distant air coils
I think you are looking for Ampere's law and Faraday's law, parts of Maxwell's equations.

For a distance D between coils much greater than the coil diameter,
The voltage induced on the second coil from a given current on the input coil is something like


Vout = 2 &pi; f N S Bo cos b,


where


f = carrier frequency of transmitted signal in Hz
N = number of turns in the receiving output coil
S = area of output loop in m^2
Bo = strength of the arrival magnetic field
b = angle of the output coil away from "axis pointing directly at input coil"


and in turn,


Bo = &mu;0 I N R^2 cos a / ( 2( R^2 + D^2 )^3/2 ),


where


&mu;0 = the universal permeability of free space
I = current in input wire
N = number of turns in the transmitting coil
R = radius of transmitting coil
D = distance between the coils
a = angle of the transmitting coil axis away from "axis pointing directly at output coil"


At long distances, the magnetic field (and hence the produced voltage) drops off with D^(-3).


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