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Mutual Inductance of two coaxial coils

  1. Jun 17, 2017 #1
    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 [​IMG] and mimetex.gif .

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

    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. jcsd
  3. Jun 17, 2017 #2

    scottdave

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    Last edited: Jun 17, 2017
  4. Jun 17, 2017 #3
    If one coil is put inside the other, and have the same cross section, are they not coaxial?! Meaning, having the same axis?
     
  5. Jun 18, 2017 #4

    scottdave

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    OK. I see your use of the terminology. It made me think of coax style cable, though.
     
  6. Jun 18, 2017 #5
    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 [itex] \Phi_1 = L_2 I_1 [/itex], which, im pretty sure is not the right answer.
     
  7. Jun 18, 2017 #6

    haruspex

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  8. Jun 18, 2017 #7

    scottdave

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  9. Jun 18, 2017 #8
    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..
     
  10. Jun 18, 2017 #9

    scottdave

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  11. Jun 18, 2017 #10
    Thanks, that definitely helps.
     
  12. Jun 18, 2017 #11

    haruspex

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