Magnetic properties of materials

Hold a strong magnet near a steel paperclip and it leaps to your fingers. Hold it near a copper coin, an aluminium spoon, or a glass of water, and — if your magnet and your instruments are sensitive enough — you will find that even these "non-magnetic" objects respond, just far too weakly to notice with the naked eye. Every atom in every material carries orbiting and spinning electrons, and every one of those electrons is a tiny current loop with its own magnetic moment. What differs from substance to substance is not whether atoms have this microscopic magnetism, but how those countless tiny moments behave when you switch an external field on: whether they resist it, weakly go along with it, or lock together into a cooperative response millions of times stronger than either. This is the question this article answers. Building on the magnetisation $\vec M$ , magnetic intensity $\vec H$ , and susceptibility $\chi$ of the previous section, we sort real materials into three families — diamagnetic, paramagnetic, and ferromagnetic — using nothing more than the sign and size of $\chi$ , and we ask what happens to each family as you heat it. Along the way you will see why a superconductor floats above a magnet, why liquid oxygen visibly clings between the poles of a horseshoe magnet, why a red-hot iron nail stops being magnetic, and why the everyday phrase "magnetic material" quietly means only one of the three families you are about to meet. By the end you should be able to look at a measured $\chi$ or $\mu_r$ and instantly name the material's class, explain in one sentence why iron is a thousand times more strongly magnetic than aluminium, and describe — in words, not formulas — what happens at the Curie point.

Key takeaways

Every material responds to a magnetic field to some degree; the response is classified by the sign and magnitude of the magnetic susceptibility $\chi$ , where $\vec M = \chi \vec H$ .
Diamagnetic materials have small negative $\chi$ (of order $-10^{-5}$ ) and are weakly repelled; examples are bismuth, copper, water, gold, and — as a perfect case — superconductors.
Paramagnetic materials have small positive $\chi$ (of order $10^{-5}$ to $10^{-3}$ ) and are weakly attracted; examples are aluminium, sodium, platinum, and oxygen gas.
Ferromagnetic materials have large positive $\chi$ (hundreds to thousands) and are strongly attracted, retaining magnetisation after the field is removed; examples are iron, cobalt, nickel, and their alloys.
Relative permeability follows directly from susceptibility, $\mu_r = 1 + \chi$ , since $\vec B = \mu_0(\vec H + \vec M) = \mu_0(1+\chi)\vec H$ .
Heating disrupts the ordered alignment behind paramagnetism and ferromagnetism (qualitative only, no $\chi \propto 1/T$ formula on this syllabus); above its Curie point a ferromagnet turns paramagnetic. Diamagnetism, being an induced effect, barely notices temperature.
Key idea: classify a material by the sign and size of its susceptibility $\chi$ — small negative means diamagnetic (weakly repelled), small positive means paramagnetic (weakly attracted), and $\chi$ in the hundreds or thousands means ferromagnetic (strongly attracted, with memory), and heating always works against the ordered alignment of para- and ferromagnets while leaving diamagnetism essentially untouched.

The core insight

A material's magnetic class — diamagnetic, paramagnetic, or ferromagnetic — is read directly off the sign and size of its susceptibility $\chi$ in $\vec M = \chi\vec H$ , and heat always works to disorder the aligned moments behind para- and ferromagnetism, most dramatically at a ferromagnet's Curie point.

Where it fits in the syllabus

This is the closing theme of Unit V, Magnetism and Matter, in CBSE Class 12 Physics, and it is explicitly prescribed: "Magnetic properties of materials — dia-, para-, ferromagnetic substances with examples; magnetisation; effect of temperature on magnetic properties." It leans directly on the previous node's $\vec B$ , $\vec H$ , $\vec M$ , and $\chi$ machinery, turning those definitions into a working classification you can apply to any given number. The 2025-26 syllabus keeps two things firmly out of scope here: the quantitative Curie law $\chi \propto 1/T$ (temperature effects stay qualitative — "heat disturbs magnetic order," not a formula to substitute into), and any quantitative hysteresis-loop area or energy-loss calculation. Both appear below only as ideas, never as things to compute.

The physical picture

Every atom carries electrons in motion, and moving charge always creates a magnetic moment — so, in principle, every atom is a tiny magnet. What separates the three classes is how those atomic moments interact with each other and with an applied field. In a diamagnetic atom, the individual electron moments already cancel in pairs, leaving zero net atomic moment when there is no external field. Switch a field on, and by Lenz's-law-like induction the orbiting electrons adjust their motion just enough to create a small induced moment that opposes the applied field. The response is present in literally every atom, but it is so small that it is masked whenever a stronger para- or ferromagnetic response exists in the same material. In a paramagnetic atom, unpaired electrons leave a small permanent atomic moment even with no field applied — but with the field off, thermal jostling points these atomic moments in random directions, so the material shows no bulk magnetisation. Switch a field on, and each atomic moment feels a small torque nudging it to align with the field (opposed by thermal randomisation), producing a small net magnetisation along the field. In a ferromagnetic material, strong quantum-mechanical interactions between neighbouring atoms lock large clusters of atomic moments — called domains — into a common direction even with no applied field, though different domains point differently so the bulk sample can appear unmagnetised overall. An external field does not have to fight thermal randomisation one atom at a time; it only has to persuade whole domains to swing into alignment or grow at the expense of misaligned neighbours, which is why the response is enormous and why some alignment can survive after the field is switched off. The magnetisation $\vec M$ that a material develops in a field of intensity $\vec H$ is, for these three classes at ordinary field strengths, simply proportional to $\vec H$ :

\vec M = \chi \vec H

where: $\vec M$ is the magnetic moment per unit volume induced in the material, $\vec H$ is the applied magnetic field intensity, and $\chi$ (chi), the magnetic susceptibility, is a dimensionless number that carries the sign and strength of the response. The physical reading is that $\chi$ is the single number that tells you everything about a material's class: negative and tiny for diamagnets, positive and tiny for paramagnets, positive and huge for ferromagnets. The total field $\vec B$ inside the material folds in both the applied intensity and the material's own response:

\vec B = \mu_0(\vec H + \vec M)

where: $\vec B$ is the resultant magnetic field inside the material, $\mu_0 = 4\pi\times10^{-7}\ \text{T}\,\cdot\,\text{m/A}$ is the permeability of free space, and $\vec H + \vec M$ combines the externally applied intensity with the material's induced response. The physical reading is that a diamagnet's negative $\vec M$ slightly reduces $\vec B$ inside it relative to free space, while a paramagnet's or ferromagnet's positive $\vec M$ enhances it — dramatically so for a ferromagnet.

Figure

Three panels showing atomic magnetic moments as small arrows inside a circle for diamagnetic paramagnetic and ferromagnetic materials before and after a field is applied

Derivation AFrom B, H, M to the permeability relation mu_r equals one plus chi

The goal is to derive, using only the definitions already available from the previous section, the single relation that links relative permeability $\mu_r$ to susceptibility $\chi$ — the relation every classification-and-numbers question on this topic ultimately tests. We start from the defining relation $\vec B = \mu_0(\vec H + \vec M)$ and the linear-response law $\vec M = \chi\vec H$ , and combine them using nothing beyond substitution and factoring.

Step 1. Start from the field relation inside a material, $\vec B = \mu_0(\vec H + \vec M)$ . This just says the total field is built from the applied intensity $\vec H$ plus whatever extra magnetisation $\vec M$ the material itself contributes.

Step 2. Substitute the material's linear response, $\vec M = \chi \vec H$ , into that expression: $\vec B = \mu_0(\vec H + \chi\vec H)$ .

Step 3. Factor out $\vec H$ : $\vec B = \mu_0(1+\chi)\vec H$ . The bracketed quantity, $(1+\chi)$ , is by definition the relative permeability $\mu_r$ , so that $\vec B = \mu_0\mu_r\vec H$ — the field is simply the vacuum value scaled up (or down) by $\mu_r$ .

Step 4. Read off the classification relation, $\mu_r = 1 + \chi$ . For a diamagnet, $\chi$ is a small negative number, so $\mu_r$ is a whisker below $1$ . For a paramagnet, $\chi$ is a small positive number, so $\mu_r$ is a whisker above $1$ . For a ferromagnet, $\chi$ is large and positive, so $\mu_r$ can be in the hundreds or thousands — the field inside the material is hugely amplified compared to free space, which is exactly why wrapping a coil around an iron core makes such a strong electromagnet. Verified: for $\chi = -2\times10^{-5}$ (a typical diamagnet), $\mu_r = 1 + (-2\times10^{-5}) = 0.99998$ ; for $\chi = 5\times10^{-4}$ (a typical paramagnet), $\mu_r = 1.0005$ ; for $\chi = 999$ (a soft ferromagnet), $\mu_r = 1000$ — all consistent with $\mu_r = 1+\chi$ .

Effect of temperature. Heat is disorder's ally. In a paramagnet, raising the temperature gives thermal jostling more energy to knock atomic moments out of alignment with the field, so the net magnetisation for a given $H$ falls as temperature rises. In a ferromagnet the same fight happens between thermal disorder and the strong inter-atomic coupling that locks domains together — and because that coupling is so strong, ferromagnetic order survives up to a sharply defined temperature, the Curie point, above which the coupling loses the fight outright and the material's domains disorder completely; beyond the Curie point a ferromagnet behaves like an ordinary paramagnet. Diamagnetism is different in kind: it is not a thermally ordered alignment of pre-existing moments but a field-induced response of paired electrons, so it is essentially unaffected by temperature. The syllabus asks only for this qualitative picture — not the formal Curie law $\chi \propto 1/T$ , which stays out of scope.

Worked examples

Board level - classifying a rod from its measured relative permeability

A rod of unknown material has measured relative permeability $\mu_r = 0.99998$ . (a) Classify the material. (b) Estimate its susceptibility $\chi$ . (c) State whether it would be attracted to or repelled by a strong magnet.

Step 1. Use the relation just derived, $\mu_r = 1+\chi$ , rearranged to $\chi = \mu_r - 1$ .

Step 2. Substitute the given value: $\chi = 0.99998 - 1 = -2\times10^{-5}$ .

Step 3. Classify by the sign and size of $\chi$ . Since $\chi$ is negative and very small in magnitude ( $10^{-5}$ scale), the material is diamagnetic.

Step 4. Interpret physically. Diamagnetic materials are weakly repelled by an external field. Answer: the material is diamagnetic, with $\chi \approx -2\times10^{-5}$ , and it would be very weakly repelled by a strong magnet — an effect far too small to feel by hand, though detectable with sensitive apparatus.

Competitive level - Curie-point transition and a magnetisation ratio

A sample is placed in a fixed magnetic intensity $H = 2\times10^{3}\ \text{A/m}$ . At room temperature its magnetisation is measured as $M_1 = 1.8\times10^{6}\ \text{A/m}$ . The sample is then heated steadily; its magnetisation falls sharply once it crosses about $770\ ^\circ\text{C}$ , settling to a much smaller value $M_2 = 3.0\times10^{2}\ \text{A/m}$ just above that temperature. (a) Identify the transition and the likely material. (b) Find the susceptibility $\chi_1$ below the transition and classify that regime. (c) Find $\chi_2$ just above the transition and classify that regime. (d) Find the ratio $M_1/M_2$ and comment on what it shows about domain alignment.

Step 1. Identify the transition. A sharp collapse in magnetisation at one specific critical temperature is the signature of a ferromagnetic-to-paramagnetic transition at the Curie point; a Curie point near $770\ ^\circ\text{C}$ ( $\approx 1043\ \text{K}$ ) matches iron closely, so the sample is most likely iron or an iron-rich alloy.

Step 2. Compute $\chi_1$ below the Curie point using $M = \chi H$ , so $\chi_1 = M_1/H = (1.8\times10^{6})/(2\times10^{3}) = 900$ . This is a large positive number, consistent with strong ferromagnetic behaviour ( $\mu_{r,1} = 1+\chi_1 = 901$ ).

Step 3. Compute $\chi_2$ above the Curie point similarly: $\chi_2 = M_2/H = (3.0\times10^{2})/(2\times10^{3}) = 0.15$ . This is small and positive — the material now behaves as an ordinary paramagnet ( $\mu_{r,2} = 1.15$ ), consistent with the domains having disordered above the Curie temperature.

Step 4. Compare the two regimes: $M_1/M_2 = (1.8\times10^{6})/(3.0\times10^{2}) = 6.0\times10^{3}$ . The magnetisation collapses by a factor of six thousand across the transition — a dramatic, near-discontinuous drop, which is exactly the qualitative signature the syllabus expects you to recognise: below the Curie point strong domain alignment gives a huge $\chi$ , and above it the same sample is reduced to an ordinary weak paramagnetic response. Answer: the sample is iron undergoing its ferromagnetic-to-paramagnetic transition near the Curie point ( $\approx 770\ ^\circ\text{C}$ ); $\chi_1 = 900$ (ferromagnetic) below it, $\chi_2 = 0.15$ (paramagnetic) above it, and the magnetisation falls by a factor of about $6000$ across the transition. Timing note: about two minutes. The whole problem is two applications of $\chi = M/H$ plus a one-line classification rule (sign and rough size of $\chi$ ) — there is no calculus and no Curie-law formula to invoke; naming the Curie point and reading off "ferromagnetic below, paramagnetic above" from the numbers is worth more marks than any extra arithmetic.

Common traps

Treating "non-magnetic" as a real category — every material has at least a diamagnetic response; what people mean by "non-magnetic" is usually "not strongly ferromagnetic."
Mixing up the direction of the force — diamagnetic materials are weakly repelled; paramagnetic and ferromagnetic materials are attracted (ferromagnetic far more strongly).
Assuming paramagnetic and ferromagnetic susceptibilities are similar in size — paramagnetic $\chi$ is typically $10^{-5}$ to $10^{-3}$ , while ferromagnetic $\chi$ can run into the hundreds or thousands; these are worlds apart, not a small difference in degree.
Trying to plug numbers into a Curie-law formula $\chi \propto 1/T$ — this syllabus keeps temperature dependence strictly qualitative; describing the trend in words is what is expected, not a calculation.
Forgetting that above the Curie point a ferromagnet does not become non-magnetic — it becomes an ordinary (weak) paramagnet, not zero response.
Confusing $\chi$ and $\mu_r$ in a numerical answer — remember $\mu_r = 1+\chi$ , so a diamagnet has $\mu_r$ just below one, not a negative $\mu_r$ .

Common trapA ferromagnet above its Curie point is not non-magnetic — and diamagnetism is not "weak ferromagnetism"

Two mistakes account for most lost marks here. First, students often assume that once a ferromagnetic material like iron is heated past its Curie point and stops behaving ferromagnetically, it becomes completely non-magnetic. It does not — it becomes an ordinary paramagnet, with a small positive $\chi$ , still weakly attracted to a field, just no longer capable of the strong domain-driven response or of retaining magnetisation on its own. Second, students sometimes picture diamagnetism as simply "a very weak version of paramagnetism," differing only in degree. It differs in kind: paramagnetism comes from pre-existing atomic moments that a field merely nudges into partial alignment (a process temperature actively fights), while diamagnetism is an induced effect present in every atom, arising even in atoms with zero net moment, and it survives almost unchanged as temperature rises. Sign, mechanism, and temperature response are all different — do not blur diamagnetic and paramagnetic into one weak-and-weaker family.

You should be able to...

Classify a material as diamagnetic, paramagnetic, or ferromagnetic given a numerical value of $\chi$ or $\mu_r$ , and state whether it is attracted or repelled.
State the relation $\mu_r = 1+\chi$ and derive it from $\vec B = \mu_0(\vec H+\vec M)$ and $\vec M = \chi\vec H$ .
Give at least two real-world examples for each of the three classes.
Explain in words why ferromagnetic materials respond far more strongly than para- or diamagnetic ones, using the idea of aligned domains.
Describe qualitatively how increasing temperature affects each class, including the Curie point for ferromagnets, without invoking a $\chi \propto 1/T$ formula.
Explain why diamagnetism, unlike para- or ferromagnetism, is essentially unaffected by temperature.

Ask the tutor: Want to work through why the frog-levitation and floating-superconductor demonstrations both come from the same diamagnetism you just learned, with the actual field strengths involved?

Why does a magnet not stick to my aluminium water bottle if aluminium is paramagnetic?

Aluminium genuinely is paramagnetic and is genuinely attracted to a strong enough field — but its susceptibility is tiny, typically around $\chi \approx 2\times10^{-5}$ , so $\mu_r$ is barely above one. The attractive force this produces is thousands of times weaker than what a ferromagnet like iron produces, because iron's $\chi$ can be in the hundreds or thousands rather than one part in a hundred thousand. A refrigerator magnet is nowhere near strong enough, and your hand nowhere near sensitive enough, to feel aluminium's real but minuscule pull. Laboratory-grade instruments with very strong fields can detect it, but everyday magnets cannot.

Is water actually magnetic? I have heard frogs can be levitated with magnets.

Yes — water is diamagnetic, with a small negative susceptibility, and the frog-levitation experiment (a real, Nobel-adjacent demonstration) is a genuine consequence of that. A sufficiently powerful magnet (tens of teslas, far stronger than any classroom magnet) can repel the water inside a living frog's body strongly enough to balance gravity and float the frog in mid-air, completely unharmed. It works precisely because diamagnetism, though universal, is normally so weak that only an extreme field can make its repulsion large enough to matter. It is a spectacular but entirely ordinary demonstration of the physics in this section, not an exception to it.

Why do superconductors count as perfect diamagnets?

Below their critical temperature, superconductors expel any applied magnetic field from their interior almost completely — a phenomenon called the Meissner effect. In the language of this section that means their susceptibility is $\chi = -1$ exactly (as close to it as measurement allows), the most extreme negative value physically possible, corresponding to $\mu_r \approx 0$ . Ordinary diamagnets like bismuth or copper only manage $\chi$ of order $-10^{-5}$ , so a superconductor's diamagnetic response is roughly a hundred thousand times stronger — strong enough that a small magnet will visibly levitate above a cooled superconducting disc, which is the standard classroom demonstration of "perfect diamagnetism."

If every atom is magnetic, why do we even bother classifying materials at all?

Because in any real material one effect always dominates the observable behaviour, even though all the underlying atomic-scale effects are simultaneously present. A paramagnetic atom's own diamagnetic response never disappears — it is just too small to notice next to the larger paramagnetic alignment happening in the same atom. Classification by class is a statement about which effect wins the competition and sets the sign and rough size of the material's overall $\chi$ , which is exactly the practically useful thing to know: will this material be pulled toward a magnet, pushed away from it, or grabbed and held. That is why the three-way classification, built from nothing more than the sign and magnitude of one number, is genuinely predictive and not an oversimplification.