There are formulae for calculating L and M in terms of Geometry of the coils.
L=(N*2)* / (l / (a *Permeability))
M12=(N1*N2) / (l /(a*Permeability ))
Then you can calculate K as expressed by you.
But when the coils are so far away as you say, the mutual inductance between the two coils will be almost negligible. There will be only more Leakage Fluxes, particularly so if the core is not a magnetic material and the Primary current is less and the number of turns are also less.
May I Know the situation where you have that picture?
Dr. P.S, This is the situation, I want to transfer power from primary coil to seconday coil but the distance between the primary coil and secondary coil must be 20m.
Since the distance between the two coils is not very much you can use wires or cable to transfer any amount of power.
If the two coils are to be isolated you can use 1:1 isolating Power transformers at any end with cable connection.
If Power at the other end is to be at a different voltage level isolation transformer and power transformers are to be used.
If the other coil is at an inaccessible place or at an hazardous place ,and if the power level is less you can use Frequency converting cyclo-converters at both ends with H.F. Transmitter and Receiver. Otherwise if the Power level is also to be high there are some recent papers on High Power Transmission over space.
The question though appears to be simple there are several answers as stated above and leads to think a lot.