Vector magnetic potential of current sheet

daudaudaudau

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.

kcdodd

No. The potential of an infinite sheet does not converge at infinity. But you can define a local potential.