Module 3 : MAGNETIC FIELD
Lecture 20 : Magnetism in Matter
  Radiation Pressure
  We have seen that electric field, as well as magnetic field, store energy. The energy density for the electric field was seen to be $(1/2)\epsilon_0E^2$ and that for the magnetic field was found to be $(1/2)B^2/2\mu_0$. For the electromagnetic waves, where $E/B =c$, the total energy density is
 
\begin{displaymath}u = \frac{1}{2}\epsilon_0E^2 +\frac{B^2}{2\mu_0} = \epsilon_0E^2\end{displaymath}
  where we have used $c^2= 1/\mu_0\epsilon_0$.
  In addition to carrying energy, electromagnetic waves carry momentum as well. The relationship between energy ( $U$) and momentum ( $p$) is given by relatistic relation for a massless photons as $p= U/c$. Since the energy density of the electromagnetic waves is given by $\epsilon_0E^2$, the momentum density, i.e. momentum per unit volume is
 
\begin{displaymath}\mid p\mid= \frac{\epsilon_0E^2}{c} = \epsilon_0\mid \vec E\times \vec B\mid\end{displaymath}

 
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