Magnetic Materials — Formula Sheet

When a magnetic dipole is placed in uniform magnetic field, it experiences a torque τ = m⃗ × B⃗

Torque magnitude

τ = mB sin θ, where θ is angle between dipole moment and field

Magnetic potential energy

U = -mB cos θ

Orbital motion of electrons creates orbital magnetic moment

m_orb = (e/2m_e)L

Relationship

B = μ₀(H + M)

Electrons contribute to atomic magnetic moment through

(1) Orbital motion: m_orbital = (e/2m_e)L where L is angular momentum, and (2) Intrinsic spin.

Magnetization M = m_net/volume represents magnetic dipole moment per unit volume.