Electromagnetic waves in detail 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?
 A: 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.
