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I would like to verify my understanding of mutual induction.

Coil 1: n1 turns per unit length, radius is r1, has a current I1

Coil 2: n2 turns per unit length, radius is r2, has a current I2 (in the same direction as I1)

r1 > r2. Coil 2 is inserted inside Coil 1. What is the mutual inductance (per unit length)?

I believe it is: M per unit length = μo*n1*n2*pi*(r2)^2

I think that the mutual inductance is the same for any of the following three scenarios:

1) Current I1 through Coil 1 only

2) Current I2 through Coil 2 only

3) Current I1 through Coil 1 and Current I2 through Coil 2 at the same time.

Is this true?