Suppose $c$ is the speed of light. A thin wire along the $z$-axis carrying a current $I$ produces a magnetic field $$\vec B = {2I\over c} \left({ -y \vec i + x \vec j \over x^2 + y^2 }\right),$$

(a) Find $\mbox{curl }\vec B$.
$\mbox{curl }\vec B =$
(Note if this is zero or not.)

(b) Does $\vec B$ satisfy the curl test? ? it does satisfy the curl test it does not satisfy the curl test

(c) Is $\vec B$ a gradient field? ? it is a gradient field it is not a gradient field