Mutual Inductance between Two Solenoids

[derek88]

Friends:

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?

 

[elegysix]

I believe mutual inductance is a property of the physical layout, and does not depend on current. So yes, 1-3 would be correct. It relates the turns and flux in one to the current induced in the other. Here is a link from MIT which is very comprehensive. I don't think I've ever heard of dM/dl.

http://web.mit.edu/8.02t/www/802TEAL3D/visualizations/coursenotes/modules/guide11.pdf