(Solved): (30 points) A uniform plane wave in air with the phasor expression of the electric field intensity ...

(30 points) A uniform plane wave in air with the phasor expression of the electric field intensity \[ \vec{E}_{i}(x, z)=\hat{y} 10 e^{-j(3 x+4 z)}(\mathrm{V} / \mathrm{m}) \] is incident upon the planar surface of a dielectric material with \( \varepsilon_{r}=4 \) occupying the half-space \( z \geq 0 \). Determine: (a) the angle of incidence; (b) the instantaneous (time-domain) expressions for the reflected electric and magnetic fields; (c) the instantaneous (time-domain) expressions for the transmitted electric and magnetic fields; (d) the average power density, \( \vec{P}_{a v e} \), carried by the wave in the dielectric medium.