Direction of electromagnetic field

[palkia]

Homework Statement

[/B]In this question, it asks for the magnetic field associated with the electromagnetic wave.

Homework Equations

The Attempt at a Solution

The magnetic field is perpendicular to Electric field but it can be in either x or z direction...how do I choose the direction.I

 

[haruspex]

Try applying Maxwell's equation, $\vec {\nabla }\times\vec E=-\frac{\partial {\vec B}}{\partial t}$.
Or cheat and take a look at https://en.m.wikipedia.org/wiki/Electromagnetic_radiation.

 

[palkia]

But in my question,why does the wave travel in -x direction

 

[haruspex]

But in my question,why does the wave travel in -x direction

That's what the question setter chose.
Note that this might flip the answer compared to the example at the link I posted.

 

[palkia]

Is it because of kx+wt or is it part of the question?

 

[haruspex]

Is it because of kx+wt

Yes, the form kx+wt tells you it is traveling in the -x direction, assuming k and w are positive.
You can figure this out by asking where the wave will move to after time Δt. This is the same as asking what change Δx in x will cancel out the change Δt in t:
sin(kx+kΔx+wt+wΔt)=sin(kx+wt) for all x.
Clearly it is kΔx=-wΔt, so the wave is traveling in the -x direction at speed w/k.

 

[palkia]

So by shfting by dt of the magnetic or electric field will tell us the direction

 

[haruspex]

So by shfting by dt of the magnetic or electric field will tell us the direction

By shifting the time base and considering what corresponding shift in x will keep the wave unchanged. If a positive change in t goes with a positive change in x then the wave is advancing in the +x direction.