# Mutual Inductance Equation

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1. Nov 24, 2016

1. The problem statement, all variables and given/known data
A toroidal solenoid with mean radius r and cross-sectional area A is wound uniformly with N1 turns. A second toroidal solenoid with N2 turns is wound uniformly on top of the first, so that the two solenoids have the same cross-sectional area and mean radius.
What is the mutual inductance of the two solenoids? Assume that the magnetic field of the first solenoid is uniform across the cross section of the two solenoids.
Express your answer in terms of the variables N1, N2, A, r, magnetic constant μ0 and others appropriate constants.

2. Relevant equations

3. The attempt at a solution
M = μ0⋅N1⋅N2⋅A this is what I have so far and I know that I need to include the r in the equation somewhere but not really sure where or why. Could somebody please explain. Thank you.

2. Nov 24, 2016

### BvU

Hi,

Could you show your work ? There seems to be a dimension missing in your M

3. Nov 24, 2016

I just used the equation $$M = u_0*A*N_1*N_2/l$$ So I assume its the l I'm missing but how does it correspond to r

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4. Nov 24, 2016

### Staff: Mentor

If the coils were linear then l would be the length of the coils, right? If that length were bent into a circle...

5. Nov 24, 2016

I'm not sure

6. Nov 24, 2016

### BvU

Check these coursenotes ( ©2004 Sen-ben Liao, Peter Dourmashkin, and John Belcher, MIT)
In particular (11.2.6) and (11.2.12) . If you confirm for yourself they are equivalent, M follows from (11.2.14)

7. Nov 24, 2016

### Staff: Mentor

If you take a line of length L and bend it to form a circle, can you find the radius of that circle?

8. Nov 25, 2016

Is l not the length of the coil with the turns already in it?

9. Nov 25, 2016

### Staff: Mentor

You're not given the length, you're given the radius r. Your answer should be put in terms of the given variables.

10. Nov 25, 2016

Yes, so I need to convert l into r

11. Nov 25, 2016

### Staff: Mentor

Yes.

12. Nov 25, 2016

I don't know how to

13. Nov 25, 2016

### Staff: Mentor

If you take a circle of radius r and cut it at one point and straighten it out into a line segment, how long is that line segment?

14. Nov 25, 2016

2*pi*r

15. Nov 25, 2016

### Staff: Mentor

Yes!

16. Nov 25, 2016

So l = 2*pi*r

17. Nov 25, 2016

### Staff: Mentor

Yes.

18. Nov 25, 2016