Module 3 : MAGNETIC FIELD
Lecture 20 : Magnetism in Matter
  To get the wave equation for $E_x$, take the derivative of eqn. (5) with respect to $z$ and substitute in eqn. (6) and interchange the space and time derivatives,
 
\begin{displaymath}\frac{\partial^2 E_x}{\partial z^2} = \mu_0\epsilon_0 \frac{... ...z}\right)= \mu_0\epsilon_0 \frac{\partial^2 E_x}{\partial t^2}\end{displaymath}
  Similarly, we can show, We get
 
\begin{displaymath} \frac{\partial^2 B_y}{\partial z^2} = \mu_0\epsilon_0 \frac{\partial^2 B_y}{\partial t^2} \end{displaymath}
  Each of the above equations represents a wave disturbance propagating in the z-direction with a speed
 
\begin{displaymath}c = \frac{1}{\sqrt{\mu_0\epsilon_0}}\end{displaymath}
  On substituting numerical values, the speed of electromagnetic waves in vacuum is $3\times 10^{8}$ m/sec.
  Consider plane harmonic waves of angular frequency $\omega$ and wavlength $\lambda=2\pi/k$. We can express the waves as
 
\begin{eqnarray*} E_x &=& E_0\sin(kz-\omega t)\\ B_y &=& B_0\sin(kz-\omega t) \end{eqnarray*}

 
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