In region \(1, z<0, \epsilon_{1}=2 \times 10^{-11} \mathrm{~F} / \mathrm{m},
\mu_{1}=2 \times 10^{-6} \mathrm{H} / \mathrm{m}\), and \(\sigma_{1}=\)
\(4 \times 10^{-3} \mathrm{~S} / \mathrm{m} ;\) in region \(2, z>0,
\epsilon_{2}=\epsilon_{1} / 2, \mu_{2}=2 \mu_{1}\), and \(\sigma_{2}=\sigma_{1}
/ 4\). It is
known that \(\mathbf{E}_{1}=\left(30 \mathbf{a}_{x}+20 \mathbf{a}_{y}+10
\mathbf{a}_{z}\right) \cos 10^{9} t \mathrm{~V} / \mathrm{m}\) at
\(P\left(0,0,0^{-}\right) \cdot(a)\)
Find \(\mathbf{E}_{N 1}, \mathbf{E}_{t 1}, \mathbf{D}_{N 1}\), and
\(\mathbf{D}_{t 1}\) at \(P_{1} \cdot(b)\) Find \(\mathbf{J}_{N 1}\) and
\(\mathbf{J}_{t 1}\) at \(P_{1} \cdot(c)\) Find \(\mathbf{E}_{t 2}\),
\(\mathbf{D}_{t 2}\), and \(\mathbf{J}_{t 2}\) at \(P_{2}\left(0,0,0^{+}\right)
.(d)\) (Harder) Use the continuity equation to help show that \(J_{N 1}-J_{N
2}=\partial D_{N 2} / \partial t-\partial D_{N 1} / \partial t\), and then
determine \(\mathbf{D}_{N 2}\)
\(\mathbf{J}_{N 2}\), and \(\mathbf{E}_{N 2}\).