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How to find inductance of a coil with two concentric ferromagnetic cores?

  1. Nov 30, 2012 #1
    1. The problem statement, all variables and given/known data

    This isn't exactly a homework question so there aren't any data/numbers to work with. I just want to know what to do if there are two ferromagnetic cores inside a coil of wire, arranged as concentric cylinders. Or how to account for the air gap between the core and the coil?

    2. Relevant equations

    L = μN2A/l

    3. The attempt at a solution

    Should it be treat as a series circuit? Or maybe parallel? Or do you weight the contributions of the relative permeabilities by the fraction of the area inside the coil they occupy?
     
  2. jcsd
  3. Nov 30, 2012 #2

    berkeman

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    Staff: Mentor

    Depending on the arrangement, I would guess that the outer core would dominate the inductance -- that is, very little of the B-field would be coupled to the inner core. The outer core would act as a shield for the inner core, IMO.

    Do you have an application in mind?
     
  4. Nov 30, 2012 #3
    Well for example to account for the ring of air around a metal core in a solenoid. In some cases this may not be negligible.
     
  5. Nov 30, 2012 #4

    berkeman

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    Staff: Mentor

    That's a different situation than the question in your original post (OP). If you have an air gap between the windings and a single core, then that increases the leakage inductance Lk and reduces your magnetizing inductance Lm.
     
  6. Nov 30, 2012 #5
    I did put the air gap bit in my original question as well. How would you find the inductance of a coil with a metal core and an air gap around it? I don't want to assume it is negligible because it isn't always. Do you just use the relative permeabilities weighted by the areas occupied by the core and air gap?
     
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