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

<br /> \mathbf A=\frac{\mu_0}{4\pi}\int_{V&#039;}\frac{\mathbf J}{R}dv&#039;<br />

But when I do the integral, it doesn't converge. However, if I calculate \nabla\times\mathbf A, i.e. move the \nabla\times inside the integral, it works out fine. Is it really impossible to calculate \mathbf A for an infinite current sheet? I have the same problem if I try to calculate the potential V of an infinite sheet of charge, but for the electric field \mathbf E it works out fine.

 

[kcdodd]

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