Module 3 : MAGNETIC FIELD
Lecture 20 : Magnetism in Matter
The magnetization current is called bound current because the electron is not free to move through the material as they would in a conductor, but are attached to a particular atom or molecule.
  If, however, the magnetization is not uniform within the sample, the internal currents do not cancel and a magnetization current exists even in the bulk. It can be shown that the bound current density $\vec J_b$ is given by
 
\begin{displaymath}\vec J_b = \vec\nabla\times\vec M\end{displaymath}
  Ampere's Law in Presence of Magnetization
  Since magnetization of a material produces bound current, it would modify Ampere's law for magnetic field. Consider a solenoid wound around a hollow cylinder with $n$ turns per unit length carrying a current $I$. The magnetic field in the solenoid is uniform and is given by $B = \mu_0 nI$. If now, a magnetic material is inserted in the hollow of the cylinder, the material gets magnetized with a magnetization $\vec M$. The surface current density $\vec K$ has a magnitude $M$ and has the dimension of current per unit length.
  A unit length of the solenoid has an effective current given by the sum of free current $nI$ and the magnetization current $M$. Ampere's law would then give the magnetic field in the solenoid as
   
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