Magnetic field from vector potential How do you find the magnetic field from knowing the vector potential?
I have the vector potential:
$\vec{A}(x,y)=\frac{\mu_0Ixy}{\pi a^2}$
And have been asked to find the magnetic field which I happen to know is
$\vec{B}=\frac{\mu_0I}{\pi a^2}\rho(\cos{2\psi}\vec\rho - \sin2\psi\vec\psi$ (in cylindrical coordinates)
where $\vec\rho,\vec\psi$ are unit vectors.
My question is how do you get from the magnetic potential to magnetic potential

By calculating the curl
$$\vec{B}=\vec{\nabla}\times\vec{A}$$
BTW, this question probably suits more Physics.SE.
