From Maxwell's curl equations, obtain the particular differential equations for the case of $\vec{J} = J_z(y,t)\hat{z}$.
The solution provided for this question shows something like this:
$\begin{vmatrix} \vec{a_x}&\vec{a_y}&\vec{a_z}\\ 0&\frac{\partial}{\partial y}&0\\ {E_x}&{E_y}&{E_z}\\ \end{vmatrix} = -\frac{\partial \vec{B}}{\partial t}$ and $\begin{vmatrix} \vec{a_x}&\vec{a_y}&\vec{a_z}\\ 0&\frac{\partial}{\partial y}&0\\ {H_x}&{H_y}&{H_z}\\ \end{vmatrix} = \vec{J}+\frac{\partial \vec{D}}{\partial t}$
Why does the $\nabla$ have components with 0 value?