(Solved): In a vacuum, there exists a uniform plane wave with an electric field E(z)= 1000ej0za^x ...

In a vacuum, there exists a uniform plane wave with an electric field $\vec{E}(z)=$ $1000e^{-j{\beta }_{0}z}{\hat{a}}_x$ Volt/meter, which has a frequency of $20\mathrm{MHz}$. (a) In which direction does this wave propagate? (b) What is the amplitude of this wave? (c) Determine the $\vec{B}$ and $\vec{H}$ fields associated with this wave. (c) Express $\vec{E},\vec{B}$, and $\vec{H}$ in their real-time forms. (d) Find ${\beta }_0$, the phase velocity, and the wavelength of the electromagnetic wave.