Interaction among inductors

In practical electrical circuits, there is almost always some mutual inductance between or among coils when they are wound in a cylindrical shape. The magnetic fields extend significantly outside solenoidal coils, and mutual effects are almost inevitable. The same is true between and among lengths of wire, especially at very-high, ultra-high, and microwave radio frequencies. Sometimes, mutual inductance is all right, and doesn’t have a detrimental effect on the behavior of a circuit. But it can be a bad thing. Mutual inductance can be minimized by using shielded wires and toroidal inductors. The most common shielded wire is coaxial cable. 

Coefficient of coupling

The coefficient of coupling, specified by the letter k, is a number ranging from 0 (no coupling) to 1 (maximum possible coupling). Two coils that are separated by a sheet of solid iron would have essentially k = 0; two coils wound on the same form, one right over the other, would have practically k = 1.

Mutual inductance

The mutual inductance is specified by the letter M and is expressed in the same units as inductance: henrys, millihenrys, microhenrys, or nanohenrys. The value of M is a function of the values of the inductors, and also of the coefficient of coupling.
For two inductors, having values of L₁ and L₂ (both expressed in the same size units), and with a coefficient of coupling k, the mutual inductance M is found by multiplying the inductance values, taking the square root of the result, and then multiplying by k. Mathematically,

M = k (L₁L²)^1/2