Split from a 2021 class note on spin, magnetic moment, and gyromagnetic ratio.

Magnetic moment is a vector for how much an object wants to interact with an outside magnetic field. The object can be a molecule, an atom, a nucleus, or a smaller particle. For these, people also say magnetic dipole moment (μ), like a tiny bar magnet with a north and a south pole.

μ tries to line up with B0. To get there it has to fight torque, μ × B0. Lined up with B0 is the lowest energy, no torque. Pointing the other way is the highest energy. The energy is E = - μ·B0.

Bar magnet dipole next to B0 under torque, then μ parallel to B0 (low energy) and opposed (high energy)
μ as a tiny bar magnet. Torque pulls it toward B0. Parallel is low energy; opposed is high energy.

Spin was the last note. Gyromagnetic ratio is next: the constant that ties μ to I.

中文

從 2021 年那篇課間筆記拆出來的。

磁矩是一個向量，描述物體有多想跟外加磁場互動；物體可以是分子、原子、原子核，或更小的粒子。對這些來說，人也叫 magnetic dipole moment (μ)，像一顆有北極、南極的小磁鐵。

μ 想對齊 B0，要到那個方向得對抗 torque，μ × B0；跟 B0 同向是最低能量，沒有 torque，反向是最高能量，能量是 E = - μ·B0。

上一則是 spin；下一則是旋磁比：把 μ 跟 I 綁在一起的那個常數。