5.28 A uniform current density given by \mathbf{J}=\mathbf{z} J_{0} \quad\left(\mathrm{~A} / \mathrm{m}^{2}\right) gives rise to a vector magnetic potential \Lambda=-\hat{z} \frac{\mu_{0} J_{0}}{4}\left(x^{2}+y^{2}\right) \quad(\mathrm{Wb} / \mathrm{m}) (a) Apply the vector Poisson's

equation to confirm the above statement. (b) Use the expression for A to find H. (c) Use the expression for J in conjunction with Ampère's law to find H. Compare your result with that obtained in part (b).