Module 3 : MAGNETIC FIELD
Lecture 20 : Magnetism in Matter
  The amplitudes $E_0$ an $B_0$ are not independent as they must satisfy eqns. (5) and (6) :
 
\begin{eqnarray*} \frac{\partial E_x}{\partial z} &=& E_0 k \cos(kz-\omega t)\\ \frac{\partial B_y}{\partial t} &=& -B_0 \omega \cos(kz-\omega t) \end{eqnarray*}
  Using Eqn. (5) we get
 
\begin{displaymath}E_0k = B_0\omega\end{displaymath}
  The ratio of the electric field amplitude to the magnetic field amplitude is given by
 
\begin{displaymath}\frac{E_0}{B_0}=\frac{\omega}{k} = c\end{displaymath}
  Fields $\vec E$ and $\vec B$ are in phase, reaching their maximum and minimum values at the same time. The electric field oscillates in the x-z plane and the magnetic field oscillates in the y-z plane. This corresponds to a polarized wave . Conventionally, the plane in which the electric field oscillates is defined as the plane of polarization. In this case it is x-z plane. The figure shows a harmonic plane wave propagating in the z-direction. Note that $\vec E, \vec B$ and the direction of propagation $\hat k$ form a right handed triad.

 
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