Magnetic Properties

Not every material is magnetic, and the ones that are do not all behave alike. To compare materials on a common footing, five linked quantities are defined: the magnetising field $\vec H$ that is applied to a sample, the permeability that measures how easily field lines pass through it, the intensity of magnetisation $\vec M$ that the sample itself develops, the resulting magnetic induction $\vec B$ inside it, and the susceptibility that ties $M$ back to $H$. Each is defined in its own lettered sub-section below, and together they set u …

The magnetising field is the external magnetic field applied to a sample or specimen in order to magnetise it. It is a vector quantity, denoted $\vec H$, with SI unit A m$^{-1}$. Unlike $\vec B$ (which includes the material's own response), $\vec H$ represents only the field that would be present due to free currents (coils, solenoids) if the magnetic material itself were absent -- it is the cause, applied entirely from outside, while $\vec B$ and $\vec M$ (§3.4(C)-( …

Magnetic permeability measures a material's ability to let magnetic field lines pass through it

-- equivalently, its capacity to take on magnetisation, or the degree to which the field penetrates the substance. In free space, the (absolute) permeability is $\mu_0$; in any other medium it is denoted $\mu$. The relative permeability is the dimensionless ratio

$\mu_r = \frac{\mu}{\mu_0}$ …

When a bulk material -- made of atoms whose individual electron orbits carry tiny magnetic moments that normally point in random directions -- is placed in an external field, its atomic dipoles are induced to align, partially or fully, along the field. The net magnetic moment developed per unit volume of the material is the intensity of magnetisation, $\vec M$, a vector quantity with SI unit A m$^{-1}$:

$\vec M = \frac{\text{magnetic moment}}{\text{volume}} = \frac{\vec p_m}{V}$ …

When a substance such as a soft-iron bar is placed inside a uniform magnetising field $\vec H$, it becomes magnetised, developing its own magnetic moment. The total magnetic field (magnetic induction) inside the specimen, $\vec B$, is the sum of the field $\vec B_0$ that $\vec H$ alone would produce in vacuum and the extra field $\vec B_m$ produced by the material's own induced magnetisation:

$\vec B = \vec B_0 + \vec B_m = \mu_0\vec H + \mu_0\vec M = \mu_0(\vec H + \vec M)$ …

Magnetic susceptibility measures how easily and how strongly a material can be magnetised by an applied field. It is defined as the ratio of the intensity of magnetisation $\vec M$ induced in the material to the magnetising field $\vec H$ that produced it:

It is a dimensionless quantity. As listed in Table 3.1, most everyday materials have $|\chi_m|\sim10^{-5}$ or smaller -- some (aluminium, titanium, tungsten, oxygen) are positive (paramagnetic), others (copper, diamond, gold, mercury, silver, carbon dioxide) are negative (diamagnetic). Susceptibility is directly linked to relative permeability by $\mu_r = 1+\chi_m$ (§3.4(B)), …