Understand Coupling Coefficient k Between Two Wire Coils

[dnyberg2]

Can someone please look at this and tell me what's going on here?
I'm trying to understand the coupling coefficient k between two wire coils some d distance apart.
I found this but I am lost!

Please help!

 

[Simon Bridge]

Where did you find it? What is it you don't understand?
It looks like the coupling coefficient gets smaller with increased separation - which is expected.
The exact way that the coupling falls off depends on the exact geometry of the coils ... that will be what the integral is for. The graph axis should just be labelled K and d, not Ki and di.