# Mutual Inductance of two solenoids

1. Feb 22, 2009

1. The problem statement, all variables and given/known data
A solenoid has N1 turns, radius R1, and length L. It is so long that its magnetic field is uniform nearly everywhere inside it and is nearly 0 outside. A second solenoid has N2 turns, radius R2 < R1, and the same length L. It lies inside the first solenoid, with their axes parallel.

(a) Assume solenoid 1 carries variable current I. Computer the mutual inductance characterizing the emf induced in solenoid 2.

(b) Now assume solenoid 2 carries current I. Compute the mutual inductance to which the emf in solenoid 1 is proportional.

(c) State how the results of parts (a) and (b) compare with each other.

2. Relevant equations
E = -L (dI/dt)
E2= -M12 (dI1/dt)
E1= -M21 (dI2/dt)

3. The attempt at a solution
Thus far I have computed the mutual inductance to be M21=M12= (u0*N2*N1*pi*R2^2)/L
I am especially have trouble understanding what is meant by "characterizing the emf induced in solenoid 2". I don't know how to obtain a mutual inductance that CHARACTERIZES the emf. Likewise, I am not quite sure how to even interpret the significance of question (b).

Any help would be appreciated.

2. Feb 25, 2009