(Solved): A boundary between two dielectric media exists in the xy plane. In region ...

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A boundary between two dielectric media exists in the $x?y$ plane. In region 1 above the $x?y$ plane the permittivity is $?=4{?}_0$, while in region 2 below the $x?y$ plane the permittivity is $?=7{?}_0$. If the electric field in region one is $\hat{x}(2y)+\hat{y}(5x)+\hat{z}\left(z^2+1\right)\mathrm{V}/\mathrm{m}$ and there are no surface charges or currents on the boundary, (a) Find the electric flux density in region 1. (b) Find the electric field in region 2 at $z=0$. Can we find the electric field for other values of $z$ ? (c) Find the electric flux density in region 2 at $z=0$. (d) Find the volume charge density in region 1.