Question B.2: Compute the curl of F = −yi + xj....
Compute the curl of \mathbf{F}=-y \hat{\mathbf{i}}+x \hat{\mathbf{j}} .
Step-by-Step
\nabla \times \mathbf{F}=\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} \\ -y & x & 0 \end{array}\right|=2 \hat{\mathbf{k}}
This is the vector field on the left in Figure B.1. As you can see, the analytical approach demonstrates that the curl is in the positive \hat{k}-direction, as expected.
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