An electromagnetic wave $**$ Here is a particular electromagnetic field in free space: Ex $=0,$ Ey $=$ E$0$ sin$($kx $+$ t$),$ Ez $=0$; $(9\mathrm{.}64)$ Bx $=0,$ By $=0,$ Bz $=($E$0/$c$)$sin$($kx $+$ t$).$

$($a$)$ Show that this field can satisfy Maxwell$$s equations if and k are related in a certain way. $($b$)$ Suppose $=1010$ s$1$ and E$0=1$ kV$/$m$.$ What is the wavelength? What is the energy density in joules per cubic meter, averaged over a large region? From this calculate the power density, the energy flow in joules per square meter per second.