# 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.