# Electromagnetic waves question

1. ### Misr

391
Electromagnetic waves consist of electric and magnetic fields having the same phase

how?

2. ### BruceW

3,590
For an electromagnetic wave in vacuum, for a polarised plane wave, we have:
$$\vec{K} \wedge \vec{E} = \omega \vec{B}$$
(where $\vec{K}$ is the wavenumber, i.e. $\frac{2\pi}{\lambda}$ times by the unit vector of the wave's propagation. And $\omega$ is the angular frequency of the wave).
Therefore, the magnetic and electric fields have different direction and magnitude, but they have the same phase.
The reason you get this equation is by solving the electric and magnetic fields in a vacuum, for a polarised plane wave. It is probably also true for a non-polarised plane wave, and for a spherical wave, but I'm not sure about them.

3. ### rude man

5,648
In vacuo, they are in phase, a direct result of solving the Maxwell equations.

However: in a conducting medium they are not in phase. Also a result of solving the Maxwell equations.

4. ### Misr

391
Oh that's complicated I don't know anything about maxwell's equations
isn't there some simpler ways to explain this?

5. ### BruceW

3,590
I think the best I can do is explain the meaning of Maxwell's equations, since that is where it all comes from.
In loose terms, a changing magnetic field causes an electric field and a changing magnetic field causes an electric field.
Also, charge causes electric field and moving charges cause magnetic field. In a vacuum, there are no charges, so the electric and magnetic fields depend only on each other.

Then when we specify that the wave must be a polarised plane wave, there are even less possibilities for the form of the electromagnetic wave. In fact, the magnetic and electric fields must be perpendicular to each other. And they must both be perpendicular to the direction of wave propagation. And they must be in phase.

The reason for these things is because of the way that the changing magnetic and electric fields affect each other. And the precise way they do this is given by Maxwell's equations.

6. ### rude man

5,648
Misr - afraid not. If you're not willing or able to dig into the Maxwell equations you shouldn't be too worried about the phase relationship between E and B fields either. Is the question really so important to you? And if it is - which is great - why don't you want to go into the subject more deeply? Although I must say this - without calculus including vector calculus you won't get very far.

There is however a publication called 'The Radio Amateur's Handbook' published by ARRL, also "The AARL Antenna Book'. Both those pubs address e-m waves in a non-calculus manner, and they might answer your question adequately or they may not.

7. ### Misr

391
Well,I'm interested in digging into Maxwell's equations but I'm still at school and I have no time for something like this
I read the statement above in my text book"Electromagnetic waves consist of electric and magnetic fields having the same phase"
and I couldn't understand it but I didn't know that the subject is complicated
Thanks very much

8. ### sophiecentaur

13,698
It's complicated. Which is why we all say that J C Maxwell was such a smart chap. Some things in life just aren't that easy.

9. ### Misr

391
Yep,you are right

10. ### Claude Bile

1,479
Maxwell's equations are very much empirical. That is, we believe them because they agree with experiment so profoundly; they are not derived from a more fundamental source.

In other words, E and B fields in an EM wave have the same phase, because they just do, that's how we observe them to be.

Claude.

11. ### sophiecentaur

13,698
It has to be said that em waves are odd compared with other waves. Mechanical waves have a uniform flow of energy because the kinetic energy variations (movement) are out of phase with the potential energy variations (displacement). In em waves, the E field (regarded as potential energy) is in phase with the B field (associated with kinetic energy). The energy comes in 'bursts'. A kind of anomaly.

12. ### BruceW

3,590
The energy density of the electromagnetic field is equal to $\frac{B^2}{2\mu_0}+\frac{\varepsilon_0 E^2}{2}$ and for an electromagnetic plane wave in vacuum, we have: $\vec{K}\wedge \vec{E}=\omega \vec{B}$. If we substitute the second equation into the first, we find that the contributions to the energy density from the electric and magnetic fields are exactly equal.

So the potential energy stored in the electromagnetic field is half due to the magnetic field and half due to the electric field (in the case of zero charges).

13. ### chrisbaird

617
In regular traveling electromagnetic waves, the electric field causes the magnetic field and the magnetic field causes the electric field. They are in phase, because this what allows the wave to keep traveling, like waves down a slinky. There are situations in free space where the electric field is out of phase with the magnetic field, but this just does not create sustained traveling waves. It's like how jerking sporadically the end of a slinky does create slinky movement, but does not send traveling waves down it.