Magnetization & H, B Relation
M = χH, B = μ₀(H + M), μ_r = 1 + χ. Tune both to see effect.
Key Notes
Magnetization M is the magnetic moment per unit volume of a material: M = m/V. Units: A/m.
When a material is placed in an external field H, it develops a magnetization that adds to the total field: B = μ₀(H + M).
For LINEAR materials: M = χ·H, where χ is the magnetic susceptibility (dimensionless).
Permeability: μ = μ₀(1 + χ) = μ₀·μ_r, where μ_r is the relative permeability.
Three classes: diamagnetic (χ < 0, very small, μ_r ≈ 1), paramagnetic (χ > 0, small, μ_r ≈ 1), ferromagnetic (χ ≫ 1, very large, nonlinear).
H is determined by free currents alone; B includes contributions from magnetization.
In free space M = 0 ⇒ B = μ₀H.
Magnetization saturates in ferromagnets at high H — all spins aligned, can't increase M further.
Formulas
Magnetization
Vector — per unit volume.
B-H-M relation
Most general form.
Linear materials
μ_r = 1 + χ; works for dia and para materials.
Susceptibility ranges
Six orders of magnitude across classes.
Important Points
DON'T confuse H and B. H is intensity (free-current source), B is total flux density (includes material response).
In a solenoid: H = nI (purely from current). B = μ_r·μ₀·nI (includes core's M).
Saturation magnetization M_s is the maximum M a ferromagnet can have — all magnetic moments aligned.
Paramagnets: thermal motion fights alignment, so M ∝ B/T (Curie's law).
Ferromagnetic order disappears above the CURIE TEMPERATURE (T_C). For iron T_C ≈ 1043 K.
Linearity (M = χH) BREAKS DOWN for ferromagnets — they have hysteresis instead.
Magnetization & H, B Relation notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.