(3 points) For the FDTD approximation of fields in a thin slot of width $g$, show that the update for the magnetic field in the slot and tangential to the slot can be approximated as: \begin{equation*} H_{y,i,j,k}^{n+\frac{1}{2}} = H_{y,i,j,k}^{n-\frac{1}{2}} - \frac{\mu_o}{\Delta t} \left[ \frac{E_{x,i,j,k+1}^n - E_{x,i,j,k}^n}{\Delta z} \right] \end{equation*}