📂Electrodynamics

Self-Density and Ferromagnets

Description¹

Consider an object that appears nonmagnetic. Let us examine this object down to the atomic scale. Electrons orbiting the nucleus produce tiny currents, which give rise to magnetic phenomena. Each atom therefore has a very small magnetic dipole. However, because the orientations of the atoms are all random, summing all those dipole moments yields $0$.

$$ \mathbf{m}_{\text{net}}=0 $$

Thus, macroscopically the object exhibits no magnetization. However, if there is an external magnetic field, the individual dipoles tend to align in the same direction. Although each dipole is small, if they all point the same way a net, observable effect appears — i.e., the object becomes magnetic.

When the external magnetic field causes the magnetic dipoles to align and the object acquires net magnetization, the object is said to be magnetized. Depending on how a material responds to an external magnetic field, materials are classified into three categories.

• If the dipoles align in the same direction as the external magnetic field, the material is a paramagnet
• If the dipoles align in the opposite direction to the external magnetic field, the material is a diamagnet
• If the object remains magnetized even after the external magnetic field is removed, it is a ferromagnet

However, describing the degree of magnetization in terms of individual dipoles is not practical — they are too microscopic to count one by one. Therefore, just as we defined polarization density, we define the magnetization. The dipole moment per unit volume is denoted by $\mathbf{M}$.

$$ \mathbf{M} := \dfrac{\text{magnetic dipole moment}}{\text{unit volume}} $$

The larger the magnetization $\mathbf{M}$, the more strongly the object will become magnetized in the presence of an external magnetic field.