Magnetism and Matter — Formula Sheet

Mathematically

φ_B = Σ B · ΔS = 0 for any closed surface.

This contrasts with Gauss's law for electrostatics where flux = q/ε₀ (depends on enclosed charge).

Magnetisation M is defined as the net magnetic moment per unit volume of a material: M = m_net / V. SI unit: A/m.

When a magnetic material is placed inside a solenoid, the net field B = B₀ + B_m where B₀ is due to solenoid current and B_m is due to material.

The additional field due to material

B_m = μ₀M.

DIAMAGNETIC

χ is small and NEGATIVE (-1 ≤ χ < 0), μᵣ < 1, μ < μ₀. Examples: Bismuth, Copper, Lead, Silicon, Water, NaCl, Nitrogen.

The net magnetic flux through any closed surface is always zero: ∮ B·dS = 0.