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Vector magnetic potential of current sheet

  1. Mar 7, 2010 #1
    Hi. Say I have an infinite sheet of current. My book gives the following formula for the vector magnetic potential

    [tex]
    \mathbf A=\frac{\mu_0}{4\pi}\int_{V'}\frac{\mathbf J}{R}dv'
    [/tex]

    But when I do the integral, it doesn't converge. However, if I calculate [itex]\nabla\times\mathbf A[/itex], i.e. move the [itex]\nabla\times[/itex] inside the integral, it works out fine. Is it really impossible to calculate [itex]\mathbf A[/itex] for an infinite current sheet? I have the same problem if I try to calculate the potential [itex]V[/itex] of an infinite sheet of charge, but for the electric field [itex]\mathbf E[/itex] it works out fine.
     
  2. jcsd
  3. Mar 7, 2010 #2
    No. The potential of an infinite sheet does not converge at infinity. But you can define a local potential.
     
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