A uniform magnetic field $\mathbf{B}$ has constant strength $b$ teslas in the $z$-direction [i.e., $\mathbf{B}=\left<0,0,b\right>$ ]

(a) Verify that $\mathbf{A}=\frac12 \mathbf{B} \times \mathbf{r}$ is a vector potential for $\mathbf{B}$, where $\mathbf{r}=\left<x,y,0\right>$
(b) Calculate the flux of $\mathbf{B}$ through the rectangle with vertices $A$, $B$, $C$, and $D$ in Figure 17.

$$A=\left(4,0,2\right),\quad B=\left(4,4,0\right),\quad C=\left(0,4,0\right),$$ $$D=\left(0,0,2\right),\quad F=\left(4,0,0\right)$$ $\text{Flux}(\mathbf{B})=$