(Solved): (a) Find the Poynting vector (the magnitude and direction) for the electromagnetic wave with the f ...

(a) Find the Poynting vector (the magnitude and direction) for the electromagnetic wave with the fields \( \mathbf{E}=E_{0} \cos (k x-\omega t) \hat{\boldsymbol{y}} \) and \( \mathbf{B}=B_{0} \cos (k x-\omega t) \hat{\mathbf{z}} \), where \( E_{0}, B_{0}, k, \omega \) are known. The wave propagates in a magnetic with relative permeability \( \mu_{r} \). (b) Write down the actual (real) electric and magnetic fields for a monochromatic plane wave with electric field amplitude \( E_{0} \), angular frequency \( \omega \), and phase angle zero that is traveling in vacuum in the negative \( x \) direction and polarized in the \( z \) direction.