Magnetic dipole

Magnetic dipoles are a model of the orbital and spin motion of electrons, used to determine the magnetism of a material. These dipoles produce their own magnetic field $\vec{B}$, which tends to align with an external magnetic field.

Torque

Under an external $\vec{B}$, we get a torque:

$$\vec{T}=\vec{m}\times \vec{B}$$

where $\vec{m}$ is the magnetic dipole moment (those perpendicular arrows to the electron spin). If $\vec{T}=\vec{0}$, this implies that $\vec{m}$ is parallel to $\vec{B}$.

Why is this even useful? Consider a solenoid with $n$ turns per unit length, such that:

$${\vec{H}}_{\text{sol}}=ni\hat{z}$$

If we have a cylinder made up of some natural media, and insert it into the solenoid, the torque from $\vec{H}$ tends to align the magnetic dipole moments producing additional flux. Then:

$${\vec{B}}_{\text{sol}}-{\mu }_0{\vec{H}}_{\text{sol}}+{\vec{B}}_{\text{dipoles}}$$ $${\vec{B}}_{\text{dipoles}}={\mu }_0{\chi }_m\vec{H}$$

where ${\chi }_m$ is the magnetic susceptibility. We can think of this relationship as a cause/effect. $\vec{H}$ is the cause, and ${\vec{B}}_{\text{dipoles}}$ is the resulting effect.