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2 Types Of Magnetic Potential Energy

  1. May 24, 2015 #1
    There are 2 types of magnetic potential energy equations:
    1. ##U = -\vec \mu \cdot \vec B##
    2. ##U = \frac{1}{2} \int \mathbf{A} \cdot \mathbf{J} \, \mathrm{d}V##

    - I have searched for the second equation, only can find some information in one web site. Do you know what their names are and differences?

    - I see that second energy equation is derived from magnetic vector potential. But for the first equation, which potential equation is it derived from? Is it magnetic scalar potential?
  2. jcsd
  3. May 24, 2015 #2


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    Please explain the symbols: U, μ, A, J, V.
  4. May 26, 2015 #3


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    The first equation simply measures the mechanical work done by rotating a magetic dipole μ in a uniform magnetic feld.
    The second equation comes from the expression for field energy [itex]W=\int{\vec{H}\cdot\vec{B}}dV[/itex]. I`m looking at the derivation from that to your equation given in Sommerfeld`s book (the only one I have handy at home) but you should find it in any upper level undergrad book.
  5. May 26, 2015 #4


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    Energy, magnetic moment, vector potential, current density, volume. If you don't know what they mean, you`ll need to study a little E&M first.
  6. May 26, 2015 #5
    The first part looks good, but notice that the second equation contains the current density. I think [itex]A \cdot J[/itex] could be associated with the kinetic energy, and [itex]H \cdot B[/itex] the potential energy. These terms appear in the electromagnetic lagrangian as the magnetic components of A^J and F^*F . I'm not sure how the various tensor elements divide into potential and kinetic energy.
    Last edited: May 26, 2015
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