Module 3 : MAGNETIC FIELD
Lecture 20 : Magnetism in Matter
  Dimensions of $\vec H$ is the same as that of magnetization $\vec M$, i.e. those of A/m. Using $\oint \vec B\cdot d\vec l = \mu_0I_{\rm encl}$, and splitting $I = I_f + I_m$, where $I_f$ denotes the free current which arises due to mobile charges and $I_m$ is the magnetization (bound) current, we get
 
\begin{displaymath}\oint \vec H\cdot d\vec l = I_f\end{displaymath}
  Note that just as the displacement field in a dielectric is determined by free charges, the H-field is determined only by free currents.
  Define magnetic susceptibility $\chi$ through the relation
 
\begin{displaymath}\vec M = \chi\vec H\end{displaymath}
  Using this, we get
 
\begin{displaymath}\vec B = \mu_0(1+\chi)\vec H\end{displaymath}
  The permeability of the medium is defined as
 
\begin{displaymath}\mu = \mu_0(1+\chi)\end{displaymath}

  Exercise 1   
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