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Energy of Magnetic field by current in a long bar

  1. Dec 25, 2014 #1
    Obviously, the energy density is proportional to the square of B, which is proportional to 1/r (radius).

    Thus, the EM energy as the space integral of the energy density is infinite.

    This would suggest that a current through a very long bar cannot be realized. May I understand such a result as that current flowing through a very long bar can not be truely realized without a returning line for forming a loop?
  2. jcsd
  3. Dec 26, 2014 #2


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    Staff: Mentor

    There is a huge difference between "very long" and "infinitely long" as the divergence is very slow (logarithmic in distance). For "very long", you still have a return path somewhere which will remove the divergence.

    A current over a finite distance without a return path would accumulate charge somewhere which stops the current flow at some point.
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