Magnetic Moment

Definition §

• magnetic strength/orientation + tendency to align with magnetic field
  • vector
• spinning charge -> magnetic moment
  • electron’s magnetism caused by constantly spinning quarks
  • current -> magnetism

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

where $\tau$ is the torque on the magnet, $m$ is the magnetic moment, and $B$ is the magnetic field

Magnetic Moment of an Electron §

• spinning charge -> magnetic moment
• => angular momentum of electron -> magnetic moment
• => electron spin + electron orbital -> magnetic moment

Bohr Magneton §

$${\mu }_{\text{revolution}}=\frac{eh}{4\pi m}\sqrt{l(l+1)}$$

Spin Magnetic Momentum §

$${\mu }_{\text{spin}}=\frac{eh}{4\pi m}$$

Chemistry POV §

Schrodinger’s Equation	Atomic Model
r	n -> binding energy -> PE, KE
$\theta$	$l$ -> angular momentum -> KE
$\varphi$	$m_l,m_s$ -> $\mu$