A time$-$harmonic electromagnetic wave with the electric field $()$

Ea $5$sin z propagates in a lossless dielectric medium of e $=2\mathrm{.}0$ e$0=$$$t $0\mathrm{.}5$x

$$

$$

V m

$$

$,$ m $=$ m$0($free of sources$).$

$($a$)$ Find the complex phasor representation E of the electric field. $($b$)$ Find the complex magnetic field H$,$ using Faraday$$s law for time$-$harmonic fields. Write down the magnetic field in real time, H$($x$,$t$).$

$($c$)$ The complex fields E and H should also satisfy Amp$$re$$s law for time$-$harmonic fields. Determine the value of w in rad$/$s$.$