# Direction of electromagnetic field

#### palkia

1. Homework Statement

In this question, it asks for the magnetic field associated with the electromagnetic wave.
2. Homework Equations

3. 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

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#### haruspex

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• palkia

#### palkia

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

#### haruspex

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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

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Is it because of kx+wt
Yes, the form kx+wt tells you it is travelling 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 travelling in the -x direction at speed w/k.

• palkia

#### palkia

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

#### haruspex

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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.

• palkia