Physics · Chapter 17
Study notes aligned to the official NEB syllabus.
When a material is placed in an external magnetic field, its own atomic magnetic moments respond to that field, either strengthening it slightly, weakening it slightly, or greatly strengthening it depending on the material. This response is described using a small set of magnetic quantities, and it lets us classify every material as diamagnetic, paramagnetic or ferromagnetic.
When a material is placed in an external magnetic field of strength $H$ (the magnetising field, unit A/m), the atomic magnetic dipoles inside the material partially align with the field, and the material develops a net magnetic moment per unit volume called the magnetisation $M$ (also in A/m). The total magnetic flux density $B$ inside the material is the sum of the flux due to the external field and the flux due to the material's own magnetisation:
$$B = \mu_0(H + M)$$
where $\mu_0 = 4\pi \times 10^{-7}\ \text{T m/A}$ is the permeability of free space.
The magnetic susceptibility $\chi$ (chi) measures how easily a material can be magnetised by an external field; it is the ratio of magnetisation to magnetising field:
$$\chi = \frac{M}{H}$$
The relative permeability $\mu_r$ compares the flux density in the material to the flux density that the same field would produce in vacuum. Substituting $M = \chi H$ into $B = \mu_0(H+M)$ gives $B = \mu_0(1+\chi)H$, and since $B = \mu_0 \mu_r H$ by definition of relative permeability, this gives the key relation between the two:
$$\mu_r = 1 + \chi$$
A material that concentrates field lines strongly has $\mu_r \gg 1$ (large positive $\chi$); a material that weakly opposes field lines has $\mu_r$ slightly less than 1 (small negative $\chi$).
When a material is placed in an external magnetic field, its own atomic magnetic moments respond to that field, either strengthening it slightly, weakening it slightly, or greatly strengthening it depending on the material. This response is described using a small set of magnetic quantities, and it lets us classify every material as diamagnetic, paramagnetic or ferromagnetic.
When a material is placed in an external magnetic field of strength (the magnetising field, unit A/m), the atomic magnetic dipoles inside the material partially align with the field, and the material develops a net magnetic moment per unit volume called the magnetisation (also in A/m). The total magnetic flux density inside the material is the sum of the flux due to the external field and the flux due to the material's own magnetisation:
where is the permeability of free space.
The magnetic susceptibility (chi) measures how easily a material can be magnetised by an external field; it is the ratio of magnetisation to magnetising field:
The relative permeability compares the flux density in the material to the flux density that the same field would produce in vacuum. Substituting into gives , and since by definition of relative permeability, this gives the key relation between the two:
A material that concentrates field lines strongly has (large positive ); a material that weakly opposes field lines has slightly less than 1 (small negative ).