## Q. B.3

Compute the curl of $\mathbf{H}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}}$, or H(r) = r.

## Verified Solution

$\nabla \times \mathbf{H}=\left|\begin{array}{ccc} \hat{\mathbf{i}} & \hat{\mathbf{j}} & \hat{\mathbf{k}} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ x & y & z \end{array}\right|=\mathbf{0} .$

This, as you have probably guessed, is the vector field on the far right in Figure B.1.