Magnetisation & Magnetic Intensity

When a material is placed inside a magnetic field, the tiny atomic magnetic moments within it respond to that field — sometimes dramatically, sometimes barely at all. The degree to which a material becomes magnetised in response to an applied field is quantified by two closely related quantities: the magnetisation MM and the magnetic intensity (also called the magnetic field strength) HH. Together, these quantities help us classify all magnetic materials and predict how they will behave in real devices such as transformers, MRI machines, and electric motors. Magnetisation MM is defined as the net magnetic dipole moment per unit volume of a material. When you apply an external magnetic field, the atomic or molecular magnets inside the material tend to align with it, producing a bulk magnetic effect. The magnetic intensity HH represents the 'driving force' of an applied field, independent of the material's own response. The total magnetic flux density BB inside a material depends on both HH and MM, linking the external cause to the combined internal and external effect. Understanding magnetisation and magnetic intensity is fundamental to designing electromagnets, storing data on magnetic media, and explaining natural phenomena such as the Earth's magnetic field. Different materials — diamagnets, paramagnets, and ferromagnets — respond to HH in very different ways, and the ratio of MM to HH, called the magnetic susceptibility χm\chi_m, is the key parameter that characterises each class.

Key takeaways
  • Magnetic Dipole Moments in Matter
  • Magnetic Intensity H and the Applied Field
  • Magnetic Susceptibility
  • Relative Permeability
  • Curie's Law for Paramagnets

Magnetic Dipole Moments in Matter

Every electron in an atom contributes a magnetic dipole moment arising from two sources: its orbital motion around the nucleus and its intrinsic spin. In most materials these moments cancel out in pairs. In magnetic materials, however, some net moment per atom survives. The vector sum of all these atomic moments in a small volume element ΔV\Delta V gives a net magnetic moment Δm\Delta m. The magnetisation is then defined as M=Δm/ΔVM = \Delta m / \Delta V, with SI units of A m⁻¹.

Magnetic Intensity H and the Applied Field

The magnetic intensity HH is defined through the relationship B=μ0(H+M)\mathbf{B} = \mu_0 (\mathbf{H} + \mathbf{M}), where μ0=4π×10−7\mu_0 = 4\pi \times 10^{-7} T m A⁻¹ is the permeability of free space. In free space M=0M = 0, so B=μ0HB = \mu_0 H. Inside a magnetised material, MM adds to HH, increasing BB. The quantity HH is produced solely by free currents (currents in wires, for example), whereas MM is the material's own contribution. HH has the same SI unit as MM: A m⁻¹.

Magnetic Susceptibility

For many materials (particularly para- and diamagnets) the magnetisation is directly proportional to the applied magnetic intensity: M=χmHM = \chi_m H, where χm\chi_m is the dimensionless magnetic susceptibility. For paramagnets χm\chi_m is small and positive (e.g. χm≈10−5\chi_m \approx 10^{-5} to 10−310^{-3}); for diamagnets it is small and negative (e.g. χm≈−10−5\chi_m \approx -10^{-5}). For ferromagnets χm\chi_m can be enormous (up to 10610^6) and is not constant — MM depends on the history of the material (hysteresis).

Relative Permeability

Substituting M=χmHM = \chi_m H into B=μ0(H+M)B = \mu_0(H + M) gives B=μ0(1+χm)H=μ0μrHB = \mu_0(1 + \chi_m)H = \mu_0 \mu_r H, where μr=1+χm\mu_r = 1 + \chi_m is the relative permeability of the material. For free space μr=1\mu_r = 1. For soft iron μr\mu_r can be several thousand, explaining why iron cores dramatically increase the flux in an electromagnet. The absolute permeability is μ=μ0μr\mu = \mu_0 \mu_r.

Curie's Law for Paramagnets

For a paramagnet, thermal agitation competes with the aligning effect of HH. Pierre Curie showed experimentally in 1895 that χm=C/T\chi_m = C/T, where CC is the material-specific Curie constant and TT is the absolute temperature in kelvin. This is Curie's Law: at higher temperatures, random thermal motion disrupts alignment, so susceptibility falls. For example, if C=0.12C = 0.12 K (for a particular paramagnetic salt) and T=300T = 300 K, then χm=4×10−4\chi_m = 4 \times 10^{-4}.

The Key Equation

$$\mathbf{B} = \mu_0(\mathbf{H} + \mathbf{M})
- **$B$** — Magnetic flux density (T (tesla)): The total magnetic field, including the material's own contribution. - **$\mu_0$** — Permeability of free space (T m A⁻¹): A fundamental constant equal to $4\pi \times 10^{-7}$ T m A⁻¹. - **$H$** — Magnetic intensity (magnetic field strength) (A m⁻¹): The field produced by free currents; drives magnetisation in the material. - **$M$** — Magnetisation (A m⁻¹): Net magnetic dipole moment per unit volume of the material. ## Worked Example **Problem.** A paramagnetic material has a magnetic susceptibility $\chi_m = 3.6 \times 10^{-4}$ at room temperature. It is placed in a region where the magnetic intensity is $H = 5.0 \times 10^4$ A m⁻¹. Find (a) the magnetisation $M$ of the material, (b) the magnetic flux density $B$ inside it, and (c) how $B$ would change if the temperature were doubled (assume Curie's Law applies).

M=18 A m−1,B≈62.9 mT,ΔB≈11 μTM = 18\text{ A m}^{-1},\quad B \approx 62.9\text{ mT},\quad \Delta B \approx 11\,\mu\text{T}

**Answer.** Magnetisation $M = 18$ A m⁻¹; flux density $B \approx 62.9$ mT; doubling temperature halves $M$ to $9$ A m⁻¹ but changes $B$ by only about $11\,\mu$T.
Figure
Diagram
Magnetisation vs Applied Field H for Three Material TypesH (A m⁻¹)M (A m⁻¹)0M=0ParaDiaFerro(saturation)MsatParamagnets: small +ve slope | Diamagnets: small −ve slope | Ferromagnets: steep, non-linear, saturatingSusceptibility χm = slope of M–H graph = M/H
Origins · 1 minPierre Curie and how this was discovered
PC
Pierre Curie
1859–1906 · French

Pierre Curie systematically investigated the magnetic properties of materials as a function of temperature, discovering in 1895 that the magnetic susceptibility of paramagnets is inversely proportional to absolute temperature — a relationship now known as Curie's Law (χm=C/T\chi_m = C/T). He also discovered the Curie temperature, above which ferromagnets lose their ferromagnetic ordering and become paramagnetic. Pierre Curie was so absorbed in his scientific work that his wedding to Marie in 1895 was famously low-key — he reportedly wore his usual laboratory suit, and they used money from a gift to buy two bicycles for their honeymoon tour of rural France.

  • Diamagnetism, Paramagnetism & Ferromagnetism — These three classes of magnetic material are defined precisely by the sign and magnitude of their susceptibility χm\chi_m, making them a direct application of the M–H relationship.
  • Magnetic Hysteresis & B–H Curves — Hysteresis shows that for ferromagnets MM is not a simple function of HH but depends on the material's history — extending the concept of magnetisation into non-linear territory.
  • Magnetic Flux and Flux Density — The equation B=μ0(H+M)B = \mu_0(H + M) links magnetisation directly to flux density BB, so a solid grasp of BB and magnetic flux underpins this topic.
  • Ampère's Law — Ampère's Law defines how free currents produce HH, establishing the physical origin of the applied magnetic intensity that drives magnetisation.