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Magnetism and matter is a short chapter, but students lose marks by mixing up magnetisation, susceptibility and permeability. This post sorts them out, works a solenoid problem with three cores, and explains the hysteresis loop so that "soft" and "hard" magnetic materials make sense.
What do the syllabi actually ask for?
The NTA Syllabus for JEE (Main) 2026 lists "para-, dia- and ferromagnetic substances with examples, the effect of temperature on magnetic properties". The NEET (UG) 2026 syllabus uses the same wording, and the CBSE Class 12 physics curriculum for 2025-26 adds magnetisation of materials. The hysteresis loop is not named in any of these lists, and the current NCERT chapter on magnetism and matter does not draw it, though it does describe hard and soft ferromagnets. Treat hysteresis as background that explains those two ideas, and check the bulletin for your exam year.
How do you tell dia-, para- and ferromagnets apart?
NCERT defines everything through one relation, M = χH, where M is magnetisation (magnetic moment per unit volume), H is magnetic intensity and χ is the dimensionless susceptibility. Then B = μ₀(1 + χ)H = μ₀μᵣH, so μᵣ = 1 + χ.
Diamagnetic: χ small and negative, μᵣ slightly below 1. The sample moves from stronger to weaker field. NCERT's examples include bismuth, copper, lead, water and sodium chloride.
Paramagnetic: χ small and positive, μᵣ slightly above 1. Weakly pulled towards stronger field. Examples: aluminium, sodium, calcium, oxygen gas.
Ferromagnetic: χ very large and positive. NCERT says the relative permeability of iron, cobalt, nickel and gadolinium is over 1000.
A table of measured values from HyperPhysics at Georgia State University puts aluminium at χ = 2.2 × 10⁻⁵, copper at −1.0 × 10⁻⁵, water at −0.91 × 10⁻⁵ and bismuth at −16.6 × 10⁻⁵.
Worked example: one solenoid, three cores
A long solenoid has 500 turns per metre and carries 2.0 A. Find H, then M and B with a core of (a) aluminium, (b) bismuth, (c) iron with μᵣ = 1000.
H depends only on the windings: H = nI = 500 × 2.0 = 1000 A/m. It is the same for all three cores.
Without any core, B₀ = μ₀H = 4π × 10⁻⁷ × 1000 ≈ 1.257 × 10⁻³ T.
Aluminium: M = χH = 2.2 × 10⁻⁵ × 1000 = 0.022 A/m. B = μ₀(1 + χ)H, larger than B₀ by only 22 parts in a million.
Bismuth: M = −16.6 × 10⁻⁵ × 1000 = −0.166 A/m. M points opposite to H, and B is smaller than B₀ by about 0.017 per cent.
Iron: M = (μᵣ − 1)H = 999 × 1000 ≈ 9.99 × 10⁵ A/m, and B = μᵣμ₀H ≈ 1000 × 1.257 × 10⁻³ ≈ 1.26 T.
H did not change, but B grew a thousandfold with iron, which is why electromagnets have iron cores.
What does temperature do?
For paramagnets, NCERT explains that thermal motion scrambles the atomic dipoles, so lowering the temperature or raising the field increases magnetisation until it saturates. The quantitative form used in many problems is Curie's law, χ = C/T, with T in kelvin. If a paramagnetic salt has χ = 3.0 × 10⁻⁴ at 300 K, then at 150 K its susceptibility doubles to 6.0 × 10⁻⁴.
Ferromagnets lose their domain structure when heated and become paramagnetic above the Curie temperature. HyperPhysics lists Curie temperatures of 1043 K for iron, 627 K for nickel and 293 K for gadolinium. Diamagnetism is essentially independent of temperature, a popular one-mark question.
What is a hysteresis loop and why does it matter?
Domains are the key. NCERT describes a ferromagnet as made of regions, each magnetised in one direction, that line up and grow when a field is applied. HyperPhysics on hysteresis explains what happens next: once magnetised, the material does not return to zero magnetisation when the field is removed, and must be driven back by a field in the opposite direction. Plotting M (or B) against H through a full cycle traces a closed loop.
Three points on the loop carry the vocabulary:
Saturation: all domains aligned; M stops growing.
Retentivity (remanence): the magnetisation left when H returns to zero.
Coercivity: the reverse H needed to bring M back to zero.
Turning domains round costs energy, and the energy lost as heat in each cycle grows with the area of the loop. So:
Soft iron has a narrow loop with low coercivity. It is used for transformer cores and electromagnets, where the field reverses many times a second and losses must be small.
Hard materials such as steel and Alnico have high retentivity and high coercivity. They make permanent magnets that stay magnetised and resist demagnetising.
Domains deserve attention. In a study of Finnish lower secondary students (Kähkönen and colleagues, 2020), the critical shifts in students' mental models came during investigations of magnetic fields and the internal structure of magnets.
Common mistakes and how to avoid them
Mixing up μ and μᵣ. μ = μ₀μᵣ has units; μᵣ and χ do not.
Assuming paramagnetic χ is constant. It falls as temperature rises.
Choosing steel for a transformer core. A wide loop means large energy loss per cycle; the answer is soft iron.
Forgetting the superconductor case. NCERT notes χ = −1 and μᵣ = 0 for perfect diamagnetism (the Meissner effect).
If the domain picture still feels abstract, the Fermi Concept Library covers every concept in physics, each with its own lesson, so you can revisit magnetisation and domains before attempting problems. For the force side of the chapter, read our guide to magnetic force and right-hand-rule mistakes.
A practice routine for this chapter
Day 1: classify ten materials from NCERT's lists by the sign of χ.
Day 2: five core-in-solenoid problems, changing n, I and μᵣ.
Day 3: three Curie's law problems and one on heating a ferromagnet.
Day 4: draw and label a hysteresis loop from memory, with a soft-iron loop beside it.
Day 5: explain aloud why transformer cores are soft iron, using the word "area".
Tonight, redo the worked example with a core of μᵣ = 400 and check that B comes out near 0.50 T.
