Question

Define the magnetic susceptibility and write its relation in terms of relative magnetic permeability.

Answer 1

Dear student,
Magnetic Susceptibility: The magnetic susceptibility of a material measures the ability of the substance to acquire magnetisation when place in a magnetic field.
It is defined as the ratio of intensity of Magnetisation(M) to the magnetising field intensity(H). It is denoted by ${\chi }_m$.
${\chi }_m=M/H$
It has no units.
RELATION BETWEEN MAGNETIC PERMEABILITY AND MAGNETIC SUSCEPTIBILITY
If a linear magnetic material is subjected to the action of a magnetising field intensity H, develops a magnetisation M and magnetic induction B; then
B=${\mu }_{\circ }(\mathrm{H}+\mathrm{M})$ where ${\mu }_{\circ }$= Permeability of free space
But B=​​​​​$\mu \mathrm{H}$ where $\mathrm{\mu }=$permeability of material
Therefore,
$\mu \mathrm{H}$=${\mu }_{\circ }(\mathrm{H}+\mathrm{M})$
or $\mathrm{\mu }=$${\mathrm{\mu }}_{\circ }(1+\frac{\mathrm{M}}{\mathrm{H}})$
But $\mathrm{\mu }=$${\mu }_{\circ }$${\mathrm{\mu }}_{\mathrm{r}}$ where ${\mathrm{\mu }}_{\mathrm{r}}$=Relative permeability
therefore,
${\mu }_{\circ }$${\mathrm{\mu }}_{\mathrm{r}}$=${\mu }_{\circ }$$(1+{\mathrm{\chi }}_{\mathrm{m}})$
or
${\mathrm{\mu }}_{\mathrm{r}}$=$(1+{\mathrm{\chi }}_{\mathrm{m}})$
is the relation between Relative permeability and magnetic susceptibility.

Regards.