# Vector magnetic potential of current sheet

1. Mar 7, 2010

### daudaudaudau

Hi. Say I have an infinite sheet of current. My book gives the following formula for the vector magnetic potential

$$\mathbf A=\frac{\mu_0}{4\pi}\int_{V'}\frac{\mathbf J}{R}dv'$$

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.

2. Mar 7, 2010

### kcdodd

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