Magnetism and Matter - Para-, Dia-, and Ferro-magnetic substances

Magnetic Intensity ($H$) and Magnetization ($M$): Magnetic intensity $H$ is the external magnetic field applied, while Intensity of Magnetization $M$ is the magnetic moment per unit volume developed inside the material, expressed as $M = \frac{m_{net}}{V}$.

Magnetic Susceptibility ($\chi$): It is the ratio of the intensity of magnetization $M$ to the magnetic intensity $H$. Mathematically, $\chi = \frac{M}{H}$.

Diamagnetic Substances: These substances develop weak magnetization in a direction opposite to the external magnetic field. They have a small, negative susceptibility ($\chi < 0$) and relative permeability $\mu_r < 1$. Examples include $Bi$, $Cu$, and $H_2O$.

Paramagnetic Substances: These substances develop weak magnetization in the same direction as the external field. They have a small, positive susceptibility ($\chi > 0$) and $\mu_r > 1$. Examples include $Al$, $Na$, and $O_2$ at STP.

Ferromagnetic Substances: These substances develop strong magnetization in the direction of the field due to the alignment of 'domains'. They have very large, positive susceptibility ($\chi \gg 1$) and $\mu_r \gg 1$. Examples include $Fe$, $Co$, and $Ni$.

Curie's Law: For paramagnetic materials, the magnetic susceptibility is inversely proportional to the absolute temperature $T$. Thus, $\chi = \frac{C}{T}$, where $C$ is the Curie constant.

Curie Temperature ($T_c$): The temperature above which a ferromagnetic substance loses its ferromagnetic properties and becomes paramagnetic. The susceptibility for $T > T_c$ follows the Curie-Weiss law: $\chi = \frac{C}{T - T_c}$.

Meissner Effect: A superconductor is a perfect diamagnet with $\chi = -1$ and $\mu_r = 0$. It expels all magnetic flux from its interior.