So I have read many things on electromagnetism and I have competed in the IPhO lf 2015, got an honorable mention. That is my level of physics. Now, I have been reading many topics again, this time derivation of Planck's law for radiation. It talks about electromagnetic waves. Similarly, I have done practicals involving polarized light which also talks about electromagnetix waves. Now I realize I actially do nlt knlw what these waves are. Are the waves fluctuations of electric/magnetic fiels strenghts or are they changes of the field line direction? Or is it something else?
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A classical electromagnetic wave is a simultaneous oscillation of the electric and magnetic fields satisfying the Maxwell equations.
This oscillation can be in either the direction or the magnitude of the vectors of the vector field. For a bog-standard example of oscillating magnitude, take the linearly polarized vacuum plane wave:$$\begin{array}{c}\vec E(t) = E_0 \cos\left(2 \pi ~ \frac{x - c t}{\lambda}\right) \hat y\\ \vec B(t) = B_0 \cos\left(2 \pi ~ \frac{x - c t}{\lambda}\right) \hat z \end{array}$$with appropriate restrictions on $E_0, B_0$ depending on which unit system you're using for the Maxwell equations.
For a bog-standard example of oscillating direction and constant magnitude, use linearity to instead get the circularly polarized vacuum plane wave:$$\begin{array}{c}\vec E(t) = E_0 \left[\cos\left(2 \pi ~ \frac{x - c t}{\lambda}\right) \hat y + \sin\left(2 \pi ~ \frac{x - c t}{\lambda}\right) \hat z \right] \\ \vec B(t) = B_0 \left[\cos\left(2 \pi ~ \frac{x - c t}{\lambda}\right) \hat z - \sin\left(2 \pi ~ \frac{x - c t}{\lambda}\right) \hat y \right] \end{array}$$ which transparently maintains $|\vec E| = |E_0|$, $|\vec B| = |B_0|$ and only "waves" by changing the direction of the field lines.
You might want to say that it contains a dependence on $\vec r - c t$, but if you don't do this properly then you will miss things like standing-wave solutions.
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$\begingroup$ Would it not be better to say "A classical electromagnetic wave is a simultaneous oscillation of the electric and magnetic fields satisfying the vacuum Maxwell equations." (possibly with boundary conditions). Because that is the key of e.m. waves they are solutions for Maxwell's equations that can exist independently of source, that is a charge/current distribution. $\endgroup$ Commented Jul 20, 2015 at 22:26
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$\begingroup$ @SebastianRiese Maybe, but you want to allow the generalization for waves to exist in dielectric media etc. too, so that may also be unnecessarily pedantic. Waves are basically physically defined by carrying energy/momentum (so you'd make reference to the Poynting vector, or perhaps directly to the energy density $E^2 + B^2$) and diffracting with a certain wavelength (which is harder to really define in terms of the E and B fields). $\endgroup$– CR DrostCommented Jul 21, 2015 at 0:05
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$\begingroup$ "Waves are basically physically defined by carrying energy/momentum" waves are better defined as solutions of the wave equation. Energy and momentum of waves can be tricky. $\endgroup$ Commented Jul 21, 2015 at 7:01
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$\begingroup$ @ChrisDrost Agreed, the formulation with vacuum is not ideal, source free may be better (although that of course requires a macroscopic interpretation, averaging over small volumes and not counting the response of the medium as source). $\endgroup$ Commented Jul 21, 2015 at 11:19
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$\begingroup$ So is there a physical difference between these two types of oscillations? (Direction and magnitude) Or do they both lead to the same result? $\endgroup$ Commented Jul 21, 2015 at 19:00