Mutual Inductance of two coaxial coils

1. Jun 17, 2017

razidan

1. The problem statement, all variables and given/known data
Two coils of the same length and almost the same cross-section are put one inside the other.
Find their mutual inductance if the self-inductances are $L_1$ and .

2. Relevant equations
1) $\phi_i=L_i I_i$
2) $\phi=\iint_A \vec{B} \cdot d\vec{A}$
3) $\phi_1=M_{12} I_2$

3. The attempt at a solution

I've tried working with the equations, substituting one into the other in order to get something that looks like equation 3) but I can't seem to get it...
Thanks,

R

2. Jun 17, 2017

scottdave

Last edited: Jun 17, 2017
3. Jun 17, 2017

razidan

If one coil is put inside the other, and have the same cross section, are they not coaxial?! Meaning, having the same axis?

4. Jun 18, 2017

scottdave

OK. I see your use of the terminology. It made me think of coax style cable, though.

5. Jun 18, 2017

razidan

Thanks for the response.
I did read the link you sent me but I can't see how I can use that information.
All i am given are the self inductances of the coils. So i know how to relate between the current flowing through one and the going through it (the same coil).
I tried writing the flux of coil 1 as something that is proportional to the current in coil 2 (and so the proportionality constant will be the mutual inductance). but i know I'm doing something wrong, because everything cancels out and I'm left with $\Phi_1 = L_2 I_1$, which, im pretty sure is not the right answer.

6. Jun 18, 2017

haruspex

7. Jun 18, 2017

scottdave

8. Jun 18, 2017

razidan

No.
Firstly, from what i can tell, the geometry of the problem is very different. in the problem i posted, the coils are one inside the other. in the link, they are next to each other.
Secondly, there are no numerical values in my question. what i understand from the question is that i have to find and expression for the mutual inductance using L1 and L2 only.
The relevant equation i wrote down might be in insufficient, and maybe i'm missing something..

9. Jun 18, 2017

scottdave

10. Jun 18, 2017

razidan

Thanks, that definitely helps.

11. Jun 18, 2017

haruspex

Sure, but that just changes the coupling coefficient. As I posted, that is the only thing extra you need.