Chapter 5, Problem 28P

A uniform current density given by

$J=\hat{z}{j}_0$ (A/m²)

gives rise to a vector magnetic potential

$A=\hat{z}\frac{{\mu }_0{J}_0}{4}(x^2+y^2)$ (Wb/m).

1. (a) Apply the vector Poisson’s equation to confirm the above statement.
2. (b) Use the expression for A to find H.
3. (c) Use the expression for J in conjunction with Ampère’s law to find H. Compare your result with that obtained in part (b).