## Q. B.2

Compute the curl of $\mathbf{F}=-y \hat{\mathbf{i}}+x \hat{\mathbf{j}}$.

## Verified Solution

$\nabla \times \mathbf{F}=\left|\begin{array}{ccc} \hat{\mathbf{i}} & \hat{\mathbf{j}} & \hat{\mathbf{k}} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ -y & x & 0 \end{array}\right|=2 \hat{\mathbf{k}}$

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.