Magnetic Susceptibility and Permeability – Magnetism and Matters
The key difference between magnetic susceptibility and permeability is that magnetic permeability describes the ability of a material to support the formation of a magnetic field inside itself whereas susceptibility describes whether a material is attracted to a magnetic field or is repelled from it. Magnetic Susceptibility Magnetic Permeability

### Magnetic Susceptibility The magnetic susceptibility of a magnetic substance is defined as the ratio of the intensity of magnetisation to magnetic intensity $\chi_{ m }=\frac{ I }{ H }$

1. It is ratio of two quantities with same units $\left( Am ^{-1}\right)$ so has no units.
2. It gives the measure of ease with which a material can be magnetised by magnetising field.
3. The value of $\chi_{ m }$ depends on nature of material and temperature.
4. If H = 1 then $\chi_{ m }= I$. So magnetic susceptibility is the intensity of magnetisation developed in the substance when placed in a magnetising field of unit strength.
5. Different relations for magnetic susceptibility are

A.Volume magnetic susceptibility $\chi_{ m }=\frac{ I }{ H }$

B.Mass magnetic susceptiblity $\chi_{\text {mass }}=\frac{\chi_{ m }}{\rho}$ $\rho$ = density of material

C. Molar magnetic susceptibility $\chi_{\text {molar }}=\frac{W_{\chi_{ m }}}{\rho}$ W = atomic weight

D.Molecular magnetic susceptibility $\chi_{\text {molecular }}=\frac{W}{N}\left(\frac{\chi_{ m }}{\rho}\right)=\frac{\chi_{\text {molar }}}{ N }$

### Magnetic Permeability

The magnetic permeability of a magnetic substance is defined as the ratio of the magnetic induction to the magnetic intensity so $\mu=\frac{ B }{ H }$
1. It is a scalar with unit weber/ampere-meter or henry/meter or newton/ampere $^{2}$ and dimension $M^{1} L^{1} T^{-2} A^{-2}$
2. It is a measure of ability of a medium to allow passage of magnetic lines of force through it or measure of degree to which magnetic field can penetrate through a material.
3. Relative permeability in a material $\mu_{ r }=\frac{\mu}{\mu_{0}}=\frac{ B }{ B _{0}}=\frac{\text { number of lines of magnetic induction per unit area i }}{\text { number of lines per unit area in vacuum }}$
4. $\mu_{r}$ is a dimensionless quantity.  $\mu$ is always positive and depends of nature of material and temperature.