# Plane Waves and the Poynting Vector

## Main Question or Discussion Point

Why is it that that poynting vector is independent of distance from the source?
Is it because EM waves are plane waves?
Furthermore I do not fully understand why EM waves have to be plane waves. I understand that changing magnetic fields give rise to electric fields and vice versa, but does that constitute a constant E and B field over an infinite plane?

My book states that the intensity of the wave decreases as 1/r^2, but I don't see this anywhere in the poynting vector, and doesn't that violate the premise of a plane wave?

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Andy Resnick
Why is it that that poynting vector is independent of distance from the source?
Is it because EM waves are plane waves?
Furthermore I do not fully understand why EM waves have to be plane waves. I understand that changing magnetic fields give rise to electric fields and vice versa, but does that constitute a constant E and B field over an infinite plane?

My book states that the intensity of the wave decreases as 1/r^2, but I don't see this anywhere in the poynting vector, and doesn't that violate the premise of a plane wave?
There's a lot in your post I don't understand: the Poynting vector is defined locally, in terms of the local E and H fields- it has no information about the source.

EM waves do not *have* to be plane waves; plane waves are a solution to Maxwell's equations, and so arbitrary solutions can be decomposed into a summation of plane waves.

The intensity of the electromagnetic field, for a plane wave, does not have 1/r^2 dependence: the intensity of spherical waves do.

So if the poynting vector has no information about the source, does that mean the distance from the source doesn't matter when describing Power/Area

When I spoke of plane waves I just wanted to know why is it that EM waves can be described as plane waves. I want to build up some physical inituition of plane waves, but as of now I cannot imagine how EM waves have constant values over their infinite plane. My intuition tells me that it should decrease. Or is this where the "changing E field give rise to B field and visa versa?"

I believe when the wave propagate out from a source far away, even though it start out in spherical shape, but when the radius getting very large, the surface approx a straight plane rather than a spherical shape.

From the solution of Maxwell's equation of:

$$\nabla X \vec E \;=\; -\frac{\partial \vec B}{\partial t} \;\hbox { and }\; \nabla X \vec H \;=\; \vec J \;+\; \frac{\partial \vec D}{\partial t}$$

E and B are perpendicular to each other and the direction of propagation is perpendicular to both of them. Both E and B are in a plane that propagate in direction of the normal of the plane.

Poynting vector:

$$\vec P = \vec E X \vec H$$

at a point. It is calculated from E and B at that point. It say nothing about where the E and B come from. It tell you the EM energy density (W/unit area) and the direction of the energy flow.

These are my understanding, please correct me if I am wrong. I am studying Poynting vector also.

Last edited:
Andy Resnick