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I Magnetic dipole

  1. Jan 19, 2017 #1
    does anyone knows where this formula comes from?

    μ=½B(R^3)

    I am considering a sphere of radius R, with B its magnetic field. Who is μ?

    Thanks
     
  2. jcsd
  3. Jan 19, 2017 #2

    Baluncore

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    Starting with; μ = ½ B r3, we can apply dimensional analysis to the problem.
    B is measured in tesla = N⋅m−1⋅A−1
    Multiply B by m3 to get; μ = N⋅m2⋅A−1
    We know force; N = kg⋅m⋅s−2
    So; μ = (kg⋅m⋅s−2)⋅(m2⋅A−1)
    μ = m3⋅kg⋅s−2⋅A−1
    Which has exactly the same dimensions as;
    See tables; https://en.wikipedia.org/wiki/SI_derived_unit
    magnetic moment = weber⋅meter = m3⋅kg⋅s−2⋅A−1
    So μ is the magnetic moment.
     
  4. Jan 19, 2017 #3
    Ok, that's right. But where does it comes from?

    Starting from the classical definition for the magnetic moment for a charge distribution

    μ=∑qr

    I don't find an answer

    Thanks
     
  5. Jan 19, 2017 #4
    Are you sure that is the definition of magnetic moment?
     
  6. Jan 21, 2017 #5

    vanhees71

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    2016 Award

    We need the precise context of which problem you want to solve to help you. If you mean the induced dipole moment of a paramagnetic or diamagnetic medium by applying an external magnetic field, see Jackson, 3rd edition, Sect. 5.11.
     
  7. Jan 21, 2017 #6

    Baluncore

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    There are many well trodden paths through this field. But the OP equation seems to be one or two steps off the path.
    I agree we need more context to find the path again.
    Maybe page 2 of this article will help; http://ccmc.gsfc.nasa.gov/RoR_WWW/presentations/Dipole.pdf
    I quote:
    The first equation of the dipole field in spherical polar coordinates (r,θ,φ)
    is; B = 2 M cos θ / r3
    where M is the dipole moment, which can be positive or negative.

    From eqn (1) we get; M = ½ B r3 / cos θ
    But on the dipole axis θ = 0, so; Cos θ = 1.
    So; M = ½ B r3

    The text box in the bottom corner gives the explanation and;
    μ = 4π M / μo = M x 107.
     
    Last edited: Jan 21, 2017
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