Question B.2: Compute the curl of F = − yi + xj .

\nabla \times \underline{F}= \left | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ \frac{∂}{∂x} & \frac{∂}{∂y} & \frac{∂}{∂z} \\ -y & x & 0 \end{matrix} \right | =2 \hat{k} .

This is the vector field on the left in Figure B.2. As you can see, the analytical approach demonstrates that the curl is in the positive k̂ direction, as expected.