Fully in syllabus
Dia / para / ferroClassification, χ and μr ranges, behaviour in non-uniform fields, domains, the Curie transition, Meissner effect. All in the rationalised NCERT and in both NEET and JEE Main. Drill this properly.
Gap content
Curie's law χ = C/TThe rationalised NCERT gives only the qualitative statement that cooling raises magnetisation — the equation itself is not there. But it is still asked (AIPMT 2003, JEE Main 2019). Learn the formula, do not over-invest.
Deleted from both
Hysteresis loopRemoved from the rationalised NCERT and from the JEE Main syllabus. It survives only in older banks and in KCET, MHT-CET, WBJEE and some state boards. Recognition only unless you sit those.
Three personalitiesin syllabus
Three people when the music starts
Music starts playing at a party. Watch three different people.
The first was not dancing and does not want to. When the music gets loud she actively backs away from the speaker. She is diamagnetic — she had no rhythm of her own, and the music only made her retreat.
The second was already tapping his foot, just out of time with everything else. As the music grows louder he gradually falls into step, and drifts a little closer to the speaker. He is paramagnetic — he had his own rhythm all along, it just needed organising.
The third came with a whole dance troupe. They were already moving together in perfect formation before the music even started. When it does start, the entire troupe swings into line at once and charges towards the speaker. That is ferromagnetic — and the difference is not the individuals, it is that they were already cooperating.
The three-line summary you should be able to recite
| Class | Atoms before the field arrives | What the field does | Result |
|---|---|---|---|
| Diamagnetic | Zero moment — everything cancels | Induces a small moment opposing the field | Weakly repelled |
| Paramagnetic | Permanent moments, randomly pointing | Partly aligns them with the field | Weakly attracted |
| Ferromagnetic | Permanent moments already aligned in domains | Turns the domains and grows the aligned ones | Strongly attracted |
Everything else in this topic — the χ values, the temperature behaviour, the field-line pictures — follows from column two. Sort by what the atoms were doing to begin with, and the rest is bookkeeping.
Inside the materialin syllabus
Lab 1 · The atomic view
pick a material, then turn the knobsEvery arrow is an atom's magnetic moment. Choose a material, then raise the field and see what happens — then raise the temperature and see what heat undoes.
Things worth trying: on diamagnetic, drag the temperature slider all the way — nothing happens, because there is no order for heat to destroy. On ferromagnetic, raise the field to full and then push the temperature past the Curie point and watch your army disintegrate.
What the simulation is showing you
Diamagnetic: at zero field there are no arrows at all, because the atomic moment is genuinely zero. Turn the field on and small arrows appear pointing backwards. They are induced by the field itself, which is why they vanish the moment it is switched off — and why temperature is irrelevant.
Paramagnetic: arrows exist from the start but point everywhere, so they cancel. Field organises them; heat scrambles them. The two are in a tug of war, and M depends on who is winning.
Ferromagnetic: the arrows arrive already sorted into blocks — the domains, outlined in the simulation. Notice that the field does two jobs at once: it rotates each domain, and it makes the well-aligned domains grow at their neighbours' expense.
Diamagnetism — the reluctant onein syllabus
Two runners on a circular track
Picture two runners going round a circular track in opposite directions at exactly the same speed. From outside, their effects cancel perfectly — the track looks balanced. That is a diamagnetic atom: the electron motions cancel and the net moment is zero.
Now the field arrives, and it acts like a wind blowing round the track. One runner is helped and speeds up; the other is hindered and slows down. They are no longer balanced.
And here is the twist that surprises everyone: the leftover imbalance points against the wind, not with it. Nature pushes back. That is why the material is repelled.
NCERT's own explanation
NCERT 5.5.1 puts it precisely: diamagnetic substances are those in which the resultant magnetic moment in an atom is zero. When a field is applied, electrons whose orbital moment lies along the field slow down, and those opposite speed up.
Why that direction and not the other? Because the change happens through induced currents obeying Lenz's law — the induced effect always opposes the change that caused it. You meet Lenz properly in Chapter 6; here it simply supplies the minus sign.
The result is a net moment opposite to the applied field, hence χ < 0, hence repulsion. The effect is tiny — the interior field is reduced by roughly one part in 105.
Two facts NCERT stresses
Diamagnetism is universal. Every substance has orbiting electrons, so every substance is diamagnetic to some degree. It is simply drowned out whenever paramagnetism or ferromagnetism is also present. So the correct statement is present in all materials, but usually masked — not "only in some materials".
Examples worth memorising: bismuth, copper, lead, silicon, nitrogen (at STP), water, sodium chloride.
The superstar case — superconductors
Cool certain metals far enough and they become perfect diamagnets: χ = −1 exactly, so μr = 0 and the field inside is driven to zero. The lines are not reduced, they are completely expelled. This is the Meissner effect.
A superconductor repels a magnet and, by Newton's third law, is repelled by it — which is how magnetically levitated trains work. NCERT adds that a superconductor is simultaneously a perfect conductor and a perfect diamagnet, that no classical theory unites those two properties, and that the quantum BCS theory of Bardeen, Cooper and Schrieffer (1957) explained them.
Remember the phrase as a package: perfect diamagnet ⇒ χ = −1, μr = 0, Binside = 0.
Paramagnetism — willing but disorganisedin syllabus
A classroom of fidgeting children
Thirty children, each facing a random direction, all fidgeting constantly. Ask them to face the front and some will — but the fidgeting keeps knocking them off. The louder you ask (stronger field), the more of them comply. The calmer the room (lower temperature), the longer they stay put.
That fidgeting is heat. It is the enemy of alignment. Cool the room right down and ask loudly enough, and eventually every child faces the front. At that point asking louder achieves nothing more — they are all already facing you. That ceiling is called saturation.
What NCERT says, and what it implies
The individual atoms of a paramagnetic material possess a permanent magnetic dipole moment of their own. On account of ceaseless random thermal motion, no net magnetisation is seen. In a strong enough field, and at low temperatures, the atomic moments align and point the same way as B0.
Two levers therefore raise M: increase B or decrease T. Both improve the alignment ratio, and both run into the same ceiling at saturation, when every dipole is perfectly aligned.
Field lines get concentrated inside the sample and the interior field is enhanced — but only slightly, again about one part in 105. In a non-uniform field the sample drifts from weak field towards strong.
Examples: aluminium, sodium, calcium, oxygen (at STP), copper chloride.
A rod hangs freely between two magnetic poles, settles at right angles to the field, and drifts towards the weaker region. The rod is
Ferromagnetism — the gangin syllabus
Marching bands in a stadium
Now imagine the same crowd, but they have already organised themselves into marching bands. Within any one band, everybody is perfectly in step without anybody telling them to. Between bands, though, the directions are random — one band marches north, another west, another south.
From high above the stadium the bands cancel out, and the crowd looks unmagnetised. This is why a fresh iron nail does not stick to another fresh iron nail.
Now play the music. Two things happen at once. Every band turns to face the speakers — and the bands that were already facing the right way recruit from their neighbours and grow. Soon there is one enormous band, and the whole crowd is magnetised.
Domains, in NCERT's numbers
Ferromagnetic atoms possess a dipole moment as in a paramagnetic material. But they interact with one another so as to spontaneously align over a macroscopic volume called a domain. Explaining that cooperation needs quantum mechanics and is beyond the textbook.
Scale to remember: a typical domain is about 1 mm across and contains roughly 1011 atoms. Note that this is macroscopic — you could almost see one. A domain is not an atom.
Apply a field and the domains orient along it while those already oriented grow in size. NCERT stresses these are not speculations: sprinkle a liquid suspension of powdered ferromagnetic material on the surface and the motion can be watched under a microscope.
Examples: iron, cobalt, nickel, gadolinium, and the alloy alnico.
Hard and soft — the split that builds devices
Hard ferromagnets keep their magnetisation after the field is switched off. Alnico (iron + aluminium + nickel + cobalt + copper) and natural lodestone are hard. These become permanent magnets — compass needles, speaker magnets.
Soft ferromagnets lose it the instant the field goes. Soft iron is the classic. These become electromagnet cores and transformer cores, where the magnetism must switch off on command.
Match the property to the job: must hold on ⇒ hard. Must let go ⇒ soft. This distinction is still fully in the syllabus even though the hysteresis loop that quantifies it is not.
Heat and the Curie point
Ferromagnetism depends entirely on the cooperation between neighbours. Heat attacks cooperation. Above a characteristic temperature — the Curie temperature — the domain structure disintegrates and the material becomes a paramagnet.
Note what is not lost: the individual atoms keep their moments. Only the teamwork goes. That is exactly why the material lands in the paramagnetic class and never the diamagnetic one — a distinction NEET and JEE have both tested repeatedly.
The one number that sorts themin syllabus
The eagerness number
χ (chi, said "kai") is the eagerness number. It answers one question: when a field arrives, how keenly does this material join in?
Positive means it helps. Negative means it pushes back. Big means it goes wild. That is genuinely all there is to it — and it is enough to answer the great majority of classification questions.
| Property | Diamagnetic | Paramagnetic | Ferromagnetic |
|---|---|---|---|
| Susceptibility χ | −1 ≤ χ < 0 | 0 < χ < ε (small) | χ ≫ 1 |
| Relative permeability μr | 0 ≤ μr < 1 | 1 < μr < 1 + ε | μr ≫ 1 (>1000) |
| Permeability μ | μ < μ0 | μ > μ0 | μ ≫ μ0 |
| Field lines inside | Pushed out, field reduced | Pulled in slightly, field raised | Crowded in heavily |
| In a non-uniform field | Strong → weak | Weak → strong | Weak → strong, strongly |
| Effect of temperature | Essentially none | χ falls as T rises | Becomes para above TC |
Lab 2 · The M–H signature
slope is χOn a graph of magnetisation M against magnetising field H, the slope is χ. That makes the three classes instantly distinguishable by eye.
Negative slope ⇒ diamagnetic. Gentle positive slope ⇒ paramagnetic. Steep and curving over to a plateau ⇒ ferromagnetic, and that plateau is saturation. One glance at the slope classifies the material.
The +1 that costs marks
μr = 1 + χ, never μr = χ. The 1 is the vacuum's own contribution and it never goes away, however large χ becomes.
Test any candidate relation by setting χ = 0: it must give μr = 1 and μ = μ0, since empty space is still empty space. Examiners choose χ values like 99, 499 and 599 precisely so that adding the 1 gives a clean 100, 500 or 600 — a susceptibility ending in 9 is a strong hint that the +1 is the whole point of the question.
A material has μr = 0.9999. It is
Curie's lawgap content
Putting a number on the fidgeting
Back to the classroom. We already know that a calmer room means better alignment. Curie's law simply puts a number on it: the eagerness χ is inversely proportional to the absolute temperature.
Halve the temperature and you double the eagerness. Double the temperature and you halve it. Nothing more complicated than that.
Lab 3 · The χ–T explorer
drag the temperatureThe left graph plots χ against T; the right plots the same law against 1/T, where it straightens into a line of slope C. Switch to a ferromagnet to see the Curie–Weiss version and the divergence at TC.
Watch the left graph: the curve stays above the axis throughout, because a paramagnet never turns diamagnetic on heating. Only the steepness changes.
Three things that turn Curie's law into marks
1. Always convert to kelvin. A question quoting 27°C and 227°C means 300 K and 500 K. The ratio 300/500 is nothing like 27/227.
2. Use the constant-product form. Since χT = C, two states are linked by χ1T1 = χ2T2. You never need to compute C.
3. Check the direction before the arithmetic. Cooling must raise χ. If your answer went the other way, you inverted the ratio.
Above the Curie point — the Curie–Weiss law
Heat a ferromagnet past TC and it behaves as a paramagnet, but the residual cooperation between neighbours shifts the reference point away from absolute zero:
χ = C / (T − TC) for T > TCAs T falls towards TC from above, the denominator approaches zero and χ diverges — that blow-up marks the onset of spontaneous magnetisation. For T far above TC the TC becomes negligible and it collapses back to ordinary Curie behaviour.
The trap: subtract TC first, then treat the differences as ordinary temperatures. Forgetting to subtract is the single commonest error in Curie–Weiss problems.
A paramagnetic sample has χ = 6 × 10−3 at 300 K. At 600 K its susceptibility is
Hysteresisdeleted from NEET & JEE
A mattress that remembers
Sit on an old mattress and it sinks. Stand up and it does not spring straight back — it stays dented for a while. The mattress remembers that you sat there. The Greek word for "lagging behind" is hysteresis.
A ferromagnet does the same thing with magnetism. Push it with a field and the domains line up. Take the field away and they do not all snap back — the domain walls got stuck on their way. Some magnetism stays behind.
To flatten the dent you have to push in the opposite direction. And every time you go through a complete push-and-release cycle, a little energy is lost as heat — the same way bending a paperclip back and forth warms it up.
Lab 4 · Trace a real loop
press playThe field H sweeps back and forth while B is plotted against it. Watch the path fail to retrace itself — that failure is hysteresis. The shaded area is the energy lost per cycle.
Switch between soft and hard and watch the area readout change. That single number decides what the material is good for — and it is the whole reason transformers are not built out of permanent magnets.
Reading the loop — anchor each term to an axis
| Term | Where on the graph | What it means physically |
|---|---|---|
| Saturation | The plateau at large H | Every domain aligned; no more magnetisation available |
| Retentivity | B-axis intercept (B at H = 0) | What is left over after the field is switched off |
| Coercivity | H-axis intercept (H at B = 0) | The reverse field needed to wipe that residue out |
| Loop area | The enclosed region | Energy lost as heat, per cycle, per unit volume |
The names carry the definitions: retentivity is what is retained; coercivity is the coercion needed to erase it. And area on a graph almost always means energy — check the product of the axis units if you doubt it.
Which loop for which job
Transformer or electromagnet core → narrow loop, small area, low coercivity. It is cycled fifty times a second, so a broad loop would waste energy continuously as heat, and it must demagnetise easily each half-cycle. Soft material — soft iron.
Permanent magnet → broad loop, high retentivity, high coercivity. It is never cycled; it just has to hold on and resist stray fields. Hard material — alnico.
Note that a soft material still has a small but non-zero loop. No ferromagnet has zero hysteresis.
Worked problems and recap
Permeability from susceptibility · NEET 2020 Phase 1
μ = 4π × 10−7 × 600 = 2400π × 10−7
μ = 2.4π × 10−4 T m A−1
Susceptibility of a cube · JEE Main 2019 (11 Jan)
M = 20 × 10−6 / 10−6 = 20 A m−1
χ = 20 / (60 × 103) = 3.3 × 10−4
Curie's law · JEE Main 2019 (12 Jan)
350/300 = 7/6 ≈ 1.1667
χ2 ≈ 3.267 × 10−4
Demagnetising current from coercivity · JEE Main 2014
I = Hc/n = 3 × 103/1000 = 3 A
M = χH · μr = 1 + χ · μ = μ0μr · B = μ0(H + M) dia: −1 ≤ χ < 0 · para: 0 < χ ≪ 1 · ferro: χ ≫ 1 Curie: χ = C/T · Curie–Weiss: χ = C/(T − TC) for T > TC Perfect diamagnet: χ = −1, μr = 0, Binside = 0 (Meissner)
Six sentences that carry the whole topic
1. Sort by what the atoms were doing before the field: nothing (dia), disordered (para), already organised (ferro).
2. The sign of χ is the fastest classifier there is — negative means diamagnetic, no exceptions.
3. Diamagnetism is universal but weak, and temperature does not touch it, because there is no order to destroy.
4. Field and cold both help alignment; heat destroys it. That is Curie's law in words.
5. Above the Curie point a ferromagnet becomes a paramagnet — the atoms keep their moments, only the teamwork is lost.
6. Hysteresis loop area is energy lost per cycle: narrow for transformers, broad for permanent magnets.
How to spend your time here
Parts 1 to 6 are fully in syllabus and worth real drilling. Classification questions are among the cheapest marks in the whole chapter — one glance at the sign of χ or at whether μr sits above or below 1, and you are done. NEET has asked essentially the same question since AIPMT 2001.
Part 7 is gap content. Learn χ = C/T and χ = C/(T−TC), do a handful of ratio problems, and move on. It is not in your textbook but it is still set.
Part 8 is deleted from both NEET and JEE Main. Read it once so an old practice paper cannot ambush you, and know retentivity, coercivity and loop-area-equals-energy. Then stop — unless you are also sitting KCET, MHT-CET, WBJEE or a state board, in which case it is live and worth proper attention.