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Magnetic susceptibility and relative permeability

  1. Feb 21, 2014 #1
    1. The problem statement, all variables and given/known data
    find the derivation of
    χm=μr-1
    where Xm is the magnetic susceptibility and μ is the relative permeability.

    2. Relevant equations
    M=Xm.H
    M is the magnetization,H is the magnetic field
    μr=μ/μo
    where μo is the permeability of a vacuum,


    3. The attempt at a solution
    I don't know how to start ,I know some equations related to magnetic properties but i cannot connect them to each other to find the derivation.
     
  2. jcsd
  3. Feb 21, 2014 #2

    collinsmark

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    Hello Marwa,

    Welcome to Physics Forums! :smile:

    For convenience, I've retyped in your problem.

    Derive the formula,
    [tex] \chi_m = \mu_r - 1 [/tex]

    Relevant equations:
    [tex] \mathrm{\textbf{M}} = \chi_m \mathrm{\textbf{H}} [/tex]
    [tex] \mu = \mu_r \mu_0 [/tex]
    I'm pretty sure you will need one or two more relevant equations.
    Can you find any relevant equations that relate to the magnetic field, [itex] \mathrm{\textbf{B}} [/itex]?
    .
    .
    .
     
  4. Feb 22, 2014 #3
    Relevant equations:
    β=μH

    βo=μoH

    μr=μ/μo

    β = μoH+ μoM

    M=Xm.H
     
  5. Feb 22, 2014 #4

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    Okay, with these relevant equations,
    [tex] \mathrm{\textbf{M}} = \chi_m \mathrm{\textbf{H}} [/tex]
    [tex] \mu = \mu_r \mu_0 [/tex]
    [tex] \mathrm{\textbf{B}} = \mu \mathrm{\textbf{H}}[/tex]
    [tex] \mathrm{\textbf{B}} = \mu_0 \left( \mathrm{\textbf{H}} +\mathrm{\textbf{M}} \right)[/tex]
    you have enough to show that
    [tex] \chi_m = \mu_r - 1. [/tex]
    What have you tried so far?
     
  6. Feb 22, 2014 #5
    I have tried :

    M=Xm.H
    Xm=M/H
    Xm=Mμ/B
    as H=B/μ
    and B=μo(H+M)
    Xm=(M.μ)/μo(H+M)
    so Xm=μr.M/(H+M)
     
  7. Feb 22, 2014 #6

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    Try substituting
    M = χmH
    into
    B=μ0(H+M)​
    Then factor the H.
     
  8. Feb 22, 2014 #7
    I got it:

    B=μo(H+M)
    and M=XmH
    B=μo(H+XmH)
    B=μoH(1+Xm)
    so μH=μoH(1+Xm)
    μ/μo=μr
    Xm=1-μr

    Thank you.
     
  9. Jan 2, 2017 #8
    DERIVE THE RELATIONSHIP B = μ0(H + M)
     
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