📂Electrodynamics

Self-Density and Ferromagnets

Description¹

Let’s assume there is an object that appears to be non-magnetic at first glance. If we look into this object down to the atomic level, we find that tiny currents are created by electrons orbiting around the nucleus, which result in magnetic phenomena. This means that very small magnetic dipoles are generated in each atom. However, since the directions of the atoms are all different, summing all these dipole moments results in $0$.

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

Thus, on a macroscopic level, the object does not exhibit magnetism. But, if there is an external magnetic field, the dipole moments align in the same direction. Even though these are small dipole moments, if they all point in the same direction, a noticeable effect emerges. That is, the object becomes magnetized.

When a object becomes magnetized due to the alignment of magnetic dipoles by an external magnetic field, we say the object has been magnetized. Depending on how the object responds to the external magnetic field, it can be classified into three types:

• If the dipoles align in the same direction as the external magnetic field, it is a paramagnet.
• If the dipoles align in the opposite direction of the external magnetic field, it is a diamagnet.
• If the object continues to exhibit magnetism even after the external magnetic field is removed, it is a ferromagnet.

However, using dipoles to discuss the degree of magnetization is not appropriate because it is too microscopic, making it impossible to count each magnetic dipole. Therefore, similar to how we defined polarization density, we define magnetization. This is denoted as $\mathbf{M}$, which stands for the magnetic dipole moment per unit volume.

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

The greater the magnetization $\mathbf{M}$, the stronger the magnetism the object exhibits in the presence of an external magnetic field.