Induced Magnetism

Induced magnetism is the process by which a magnetic material becomes magnetised when placed near or in contact with a permanent magnet, without the material itself being a permanent magnet beforehand. This phenomenon occurs in ferromagnetic materials such as iron, nickel, and cobalt, where the atomic-scale magnetic domains — tiny regions in which atomic magnetic moments are already aligned — can be reoriented by an external magnetic field. The key distinction in induced magnetism is between temporary and permanent magnetisation. Soft magnetic materials like pure iron are easily magnetised by an external field but lose almost all their magnetism when that field is removed; this is temporary magnetism. Hard magnetic materials like steel retain a significant fraction of their magnetisation after the external field is removed, making them suitable for permanent magnets. Understanding this difference is essential for designing electromagnets, transformers, and data-storage devices. Induced magnetism is explained at the microscopic level by domain theory. In an unmagnetised ferromagnet, the domains are randomly oriented so their net magnetic moment is zero. An external field causes domains aligned with the field to grow at the expense of misaligned ones (domain-wall motion) and can also rotate domain magnetisation toward the field direction. The degree to which these changes are reversible determines whether the resulting magnetism is temporary or permanent.

Key takeaways
  • Ferromagnetic Domains in an Unmagnetised Material
  • Applying an External Magnetic Field
  • Magnetisation and Induced Poles
  • Magnetic Susceptibility
  • Temporary vs Permanent Magnetism: Hysteresis

Ferromagnetic Domains in an Unmagnetised Material

In an unmagnetised ferromagnetic material, the material is divided into microscopic regions called magnetic domains, each with its own magnetic moment due to the alignment of electron spins. However, the domains point in random directions, so the vector sum of all domain moments is zero and the material shows no external magnetism.

Applying an External Magnetic Field

When a strong magnet (or any source of an external field B\mathbf{B}) is brought close to or in contact with the ferromagnetic material, the external field exerts a torque on each domain's magnetic moment. Domains already roughly aligned with B\mathbf{B} begin to grow by domain-wall motion: the boundaries between domains shift so that aligned domains consume volume from misaligned ones. At higher field strengths, the remaining misaligned domains rotate toward the field direction.

Magnetisation and Induced Poles

As domains align, the material develops a net magnetic dipole moment and acquires north and south poles. The induced pole closest to the inducing magnet is always opposite in polarity to the pole of the inducing magnet, which is why magnetic materials are attracted to magnets (opposites attract). The magnetisation MM of the material is defined as the magnetic dipole moment per unit volume: M = \frac{m}{V} where mm is the total magnetic dipole moment (in A ⋅ m2\text{A}\,\cdot\,\text{m}^2) and VV is the volume.

Magnetic Susceptibility

The response of a material to an applied field is quantified by the magnetic susceptibility χm\chi_m (dimensionless): M = \chi_m H where HH is the applied magnetic field intensity (in A/m). For soft iron, χm\chi_m can be tens of thousands, meaning it magnetises very strongly. The total magnetic field inside the material is then B=μ0(H+M)=μ0(1+χm)H=μrμ0HB = \mu_0 (H + M) = \mu_0 (1 + \chi_m) H = \mu_r \mu_0 H, where μr=1+χm\mu_r = 1 + \chi_m is the relative permeability.

Temporary vs Permanent Magnetism: Hysteresis

When the external field is removed, soft magnetic materials (low coercivity) allow domain walls to spring back easily — almost all magnetisation is lost. Hard magnetic materials (high coercivity) have domain walls that are pinned by impurities and crystal defects, so domains cannot easily return to random orientations; a large residual magnetisation called the remanence BrB_r remains. The energy lost per magnetisation cycle is proportional to the area enclosed by the material's B-H hysteresis loop. Soft materials have narrow loops (low energy loss, good for transformer cores); hard materials have wide loops (high energy storage, good for permanent magnets).

The Key Equation

$$\mathbf{B} = \mu_0 (\mathbf{H} + \mathbf{M}) = \mu_0 \mu_r \mathbf{H}
- **$\mathbf{B}$** — Magnetic flux density (Tesla (T)): The total magnetic field inside the material, including the contribution from induced magnetisation. - **$\mu_0$** — Permeability of free space (H/m): A fundamental constant equal to $4\pi \times 10^{-7}$ H/m, relating B and H in a vacuum. - **$\mathbf{H}$** — Magnetic field intensity (A/m): The applied magnetic field, determined by free currents (or external magnets) alone, independent of the material. - **$\mathbf{M}$** — Magnetisation (A/m): Magnetic dipole moment per unit volume of the material, representing the material's response to the applied field. - **$\mu_r$** — Relative permeability (dimensionless): Ratio of the material's permeability to $\mu_0$; for soft iron $\mu_r$ can exceed 5000, for air $\mu_r \approx 1$. ## Worked Example **Problem.** A bar of soft iron with relative permeability $\mu_r = 4000$ is placed inside a solenoid that produces an applied field of $H = 500$ A/m. (a) Calculate the magnetisation $M$ of the iron. (b) Calculate the magnetic flux density $B$ inside the iron. (c) If the solenoid is switched off, briefly explain what happens to the magnetisation of the soft iron.

M \approx 2.0 \times 10^6 \text{ A/m},\quad B \approx 2.51 \text{ T}

**Answer.** Magnetisation $M \approx 2.0 \times 10^6$ A/m; flux density $B \approx 2.51$ T; when the external field is removed, the soft iron loses its induced magnetisation because soft iron has low coercivity — it is a temporary magnet.
Figure
Diagram
Induced Magnetism: Domain AlignmentUNMAGNETISED IRON↑↓↑↓→←→←Domains: random, net M = 0MAGNETISED IRON→→→→→→→→Domains aligned, net M ≠ 0External magnetic field B →SOFT IRON (Temporary)Low coercivity, narrow B-H loopLoses magnetism when B removedSTEEL (Permanent)High coercivity, wide B-H loopRetains remanence B_r after field offvs.
Origins · 1 minWilliam Gilbert and how this was discovered
WG
William Gilbert
1544–1603 · English

William Gilbert was the first scientist to systematically study magnetism in his landmark 1600 work De Magnete, where he distinguished between the behaviour of hard and soft magnetic materials, demonstrated that the Earth itself acts as a giant magnet, and showed that iron loses its induced magnetism more readily than magnetite. His careful experiments on magnetic induction laid the conceptual groundwork for all later work on ferromagnetism. Gilbert coined the Latin word 'electricus' (from the Greek word for amber, ēlektron) to describe materials that attract light objects when rubbed — giving us the root of the word 'electricity' — yet he is best remembered for magnetism.

  • Magnetic Fields and Field Lines — Induced magnetism requires an external magnetic field to reorient domains; understanding field lines and flux density B is prerequisite knowledge.
  • Domain Theory of Magnetism — Domain structure is the microscopic mechanism behind induced magnetism; this concept explains why ferromagnets respond differently from paramagnets.
  • Electromagnets and Solenoids — Electromagnets exploit induced magnetism in soft iron cores; the contrast between temporary and permanent magnets is directly applied in their design.
  • Hysteresis and Magnetic Materials — The B-H hysteresis loop quantifies remanence and coercivity, the key properties that distinguish temporary from permanent magnetism.