$[$EM Wave$]$ Consider a planar electromagnetic wave traveling through empty space. The $-$field

associated with this EM wave is expressed as $(,)=0$ sin$(+),$ where $0,,$ and $$ are all

positive constants.

$($a$)$ In what direction is this wave traveling? How do you know?

$($b$)$ How must the constants $$ and $$ be related in order to satisfy Maxwell$$s equations?

Tip: I.e$.,$ to describe light! Consider the velocity.

$($c$)$ What is the wavelength $$ of this wave?

I.e$.$ how far in $$ does the wave travel before returning to the same value?

$($d$)$ What is the corresponding magnetic field, $$ associated with the EM wave?

Tip: What variables is $$ a function of$?$ Write your answer in terms of given variables