Question B.3: Compute the curl of H = xi + yj + zk, or H(r) = r....
Compute the curl of \mathbf{H}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}} , or H(r) = r.
Step-by-Step
\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.
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