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Magnetic Core circuit -- Help please

  1. Aug 25, 2015 #1
    Capture.JPG

    Fm = (500)(10/27)
    = 185.185 At
    Total flux = βA
    = (0.35)(0.003)
    = 0.00105 wb
    Rm = Fm / total flux
    = 185.185 / 0.00105
    = 176366.6667 At/wb
    R(air) = (0.1 x10^-3) / (700)(4π x 10^-7)(0.003)
    = 37.894034 At/wb

    Rm = length / μA
    length = Rm x μ x A
    = (176366.6667 + 37.894034) (700) (4π x 10^-7) (0.003)
    = 0.4654206 m

    ∴ 0.4654206 - (0.1 x10^-3)
    = 0.465320 m

    My answer is not the same as the answer given in the answer key.
    Where did I do wrong?
     
  2. jcsd
  3. Aug 25, 2015 #2

    mfb

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    Why do you divide by 700 here?
     
  4. Aug 25, 2015 #3
    Rm = length / μA

    So,
    length = 0.1 x10^-3

    μ = (μr) (μo)
    = (700)(4π x 10^-7)

    A = 0.003

    I followed the formulas given to me.
     
  5. Aug 25, 2015 #4

    mfb

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    It is air, μr is 1.
     
  6. Aug 25, 2015 #5

    Hesch

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    #1: You cannot use the cross section area to anything because it's the flux density that is given ( not the flux ).

    So N*I = 185.185A = Hmean * s , s is the lengt of the whole circulation path.

    Bcore = Bairgap , so you can calculate Hairgap , and Hcore = Hairgap/700.

    sairgap = 0.1 mm.

    Now use a kind of a magnetic version of Kirchhoffs voltage law to create an equation to find score.
     
  7. Aug 26, 2015 #6
    What do you mean by the length of the circulation path?
    And why Hcore = Hairgap / 700 ?

    Sorry I still don't understand, and I am getting confused with the formula.
     
  8. Aug 26, 2015 #7

    Hesch

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    It's the length of Lcore + Lairgap.
    I suggest that you read Amperes law ( circulation integral ).
    B = μ*H , B is constant ( Bairgap = Bcore ) →

    μ0*Hairgap = μr0*Hcore

    Hcore = Hairgapr

    B is constant because it's the same flux that passes anywhere in the circuit, and there is no change in the cross section area in the circuit.
     
    Last edited: Aug 26, 2015
  9. Aug 26, 2015 #8
    Thanks! Hesch.

    I have one question.
    The magnetomotive force (Fm) produced from the coil is for the core and the air gap or just for the core only?
     
  10. Aug 26, 2015 #9

    Hesch

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    I don't know. I regard it different:
    Magnetic fields are circular fields. They bite themselves in the tail. Along a circular path you cannot say "here it is" and "here it is not".
    You could say that this Fm = N*I.
    Also you could say that

    N*I - circulationH⋅ds = 0 ( according to Kirchhoffs 2. law mentioned in #7 ( analogy ) ).

    When using Amperes law, of course you will sketch a circulation path through the middle of the core and middle of the airgap. Then you could write an equation:

    Hairgap*Lairgap + Hcore*Lcore = N*I →

    Hairgap*Lairgap + ( Hairgapr )*Lcore = N*I

    ( Hairgap = B / μ0 , B = 0.35T )

    Find Lcore.
     
    Last edited: Aug 26, 2015
  11. Aug 26, 2015 #10

    rude man

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    mmf is around the entire mag circuit. Like emf is around an electric circuit. So mmf includes everything in the closed mag circuit.
    mmf = ∑ΦR around the mag. circuit like emf = ΣiR around an electric circuit.
     
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