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Homework Help: Magnetic Energy

  1. May 10, 2008 #1
    [SOLVED] Magnetic Energy

    Whoops, never mind, i didn't use the right B field


    1. The problem statement, all variables and given/known data
    Show that the magnetic energy per unit length of a nonmagnetic wire is [tex]\frac{\mu_0 I^2 }{ 16 \pi}[/tex] (inside the wire)


    2. Relevant equations

    [tex]W = 1/2 L I^2[/tex]
    [tex]W = \int \int \int \frac{|B|^2} {2 \mu} [/tex]

    3. The attempt at a solution

    Well, At first I was going to use W = 1/2 Li^2, but then I realized that I don't know how to find the self inductance of a wire. (inside it at least)

    I know the B field of a wire, but when I try to integrate it, I get something completely different.

    [tex]W = \int_0^L \int_0^{2\pi} \int_0^a \frac{(\mu_0 I)^2} {(2 * 2\pi r)^2} rdr d \phi dz[/tex] (i'll worry about the per unit length part later)
    But as you can see that gives me a ln(a/0) which can't happen, so I'm stumped
     
    Last edited: May 10, 2008
  2. jcsd
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