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I have first learnt the concept of plane electromagnetic waves as a solution to Maxwell's equations in vacuum recently and they are usually depicted them as follows: enter image description here

Here is my confusion: in the pictures, the electric and magnetic fields are depicted as nonzero just in the axis of propagation, but is this true? I guess not, because for example, when calculating the electric flux through a rectangle in the plane where $\vec{B}$ is, it is definately nonzero; furthermore it is assumed that the value of the magnitude of the electric field is exactly the same along a ray in the direction of the magnetic field. So I think that the electric and magnetic fields in EM waves in vacuum extend infinitely towards the direction of the other one, right?

If so, why are these images depicted like this, just showing one portion of the full wave?

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    $\begingroup$ Keep in mind that your sketch is a combination of two mathematical graphs, one representing electric field strengths and the other magnetic field strengths at POINTS ALONG A LINE. The vectors represent the magnitude and direction of the fields, not their physical extent. $\endgroup$
    – R.W. Bird
    Dec 16, 2019 at 19:12
  • $\begingroup$ Alright, I think I got that now. Anyways I think this diagrams are kind of confusing in some sense. Thank you! $\endgroup$
    – Nick.25
    Dec 16, 2019 at 20:34

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Yes that illustration is only showing a portion of the full wave. The image below shows the electric field throughout space as well. You can see that the electric field is the same for all points in a plane perpendicular to the propagation direction; hence why most illustrations only draw it at one point to avoid a cluttered image.

The same is true for the magnetic field, with the difference being that it's orthogonal to both the electric field and the propagation directions.

Note that this simple picture is only true for a plane wave. More complicated wave patterns also exist, but they can always be written as a combination of different plane waves. enter image description here

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