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Inductance in a straight wire

  1. Apr 8, 2013 #1
    1. The problem statement, all variables and given/known data

    A long wire carries a current i uniformly distributed over a cross section of the wire.

    Show that the magnetic energy of a length l equals μ_0 i2 l / 16π. Describe why this doesn't depend on diameter.

    Show that the inductance for a length of the wire l associated with the flux inside the wire is μ_0 l / 8π

    2. Relevant equations

    u_B = B2/2μ_0

    U = L i2 /2

    Biot-Savart law for Field in a long wire:

    B = μ_0 i / 2 π r


    3. The attempt at a solution

    Solve for u_B as

    u_B = B2/2μ_0

    = (μ_0 i / 2 π r ) 2 / 2μ_0

    Multiply by volume of wire to find U:

    U = ( (μ_0 i / 2 π r ) 2 / 2μ_0 ) * π r^2 l

    = μ_0 i2 l / 8π

    I'm off by a factor 1/2. Any suggestions?
     
  2. jcsd
  3. Apr 8, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    You need to find B inside the wire.

    If uB is not uniform inside, integration will be necessary to find the total energy.
     
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