Module 3 : MAGNETIC FIELD
Lecture 20 : Magnetism in Matter
  These equations are to be supplemented by Lorentz force equation.
  In terms of free charges and currents, the first and the fourth of Maxwell's equations are generally expressed in terms of the vectors $\vec D$ and $\vec H$ :
 
\begin{eqnarray*} \vec\nabla\cdot\vec D &=& \rho_f\\ \vec\nabla\times\vec H &=& \vec J_f + \frac{\partial\vec D}{\partial t} \end{eqnarray*}
  with the displacement vector $\vec D$ and the H-vector defined as
 
\begin{eqnarray*} \vec D &=& \epsilon_0\vec E + \vec P\\ \vec H &=& \frac{\vec B}{\mu_0} -\vec M \end{eqnarray*}
  The polarization vector $\vec P$ and the magnetization vector $\vec M$ are related to the vectors $\vec E$ and $\vec B$ respectively by constitutive relations
 
\begin{displaymath}\vec P = \epsilon\vec E\, \hspace{5mm} \ \vec M = \chi\vec H\end{displaymath}

 
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