Gap content — still asked
Curie's law χ = C/TThe rationalised NCERT gives only the qualitative statement that cooling raises magnetisation. The equation is not in the book, but it has been set as AIPMT 2003 and JEE Main 2019, and appears throughout coaching material. Learn the formula and the ratio method; that is enough.
Deleted from NEET and JEE Main
HysteresisRemoved from the rationalised NCERT and from the JEE Main syllabus. It survives in older question banks and is live for KCET, MHT-CET, WBJEE, EAMCET, BITSAT and several state boards. For NEET 2027, read for recognition; do not drill.
Why they belong on one page anyway
They are the same physics seen from two sides. Curie's law describes what heat does to magnetic order — it destroys it, smoothly and reversibly. Hysteresis describes what happens when order is hard to move — the material lags, and the lag costs energy that turns into heat.
One is heat defeating order. The other is order refusing to move, and generating heat as a result. Understanding either one makes the other easier.
Field versus heat — the tug of wargap content
Lining up children on a windy day
You are trying to line up a class of children facing the front. You have a megaphone — that is the magnetic field, and the louder you shout, the more of them face you.
But the room is full of distractions: a wasp, someone's dog, a firework outside. That is heat. The more chaos, the more children get knocked out of line.
What actually decides the outcome is not the megaphone alone, or the chaos alone. It is the ratio of one to the other. A quiet whisper in a silent room beats a shout in a hurricane.
That ratio is the whole of Curie's law. Alignment depends on field divided by temperature — which is exactly why the temperature ends up in the denominator.
Lab 1 · The tug of war
two knobs, one ratioThe left bar is the aligning energy the field offers each dipole. The right bar is the thermal energy trying to scramble it. Only their ratio matters — try to prove that by finding two different settings that give the same alignment.
Push the field high and the temperature low and the alignment approaches 100% — saturation. Notice that Curie's law breaks down there: it only holds while alignment is small, which means while mB is much less than kT.
The honest version, for the curious
The full theory says the fraction aligned follows the Langevin function of the ratio x = mB/kT. For small x it simplifies to roughly x/3, giving
M ≈ n m2B / (3k T) ⇒ χ = μ0 n m2 / (3k T) = C/TYou are not required to derive this. But it does show two useful things: the Curie constant C is built from real material properties (how many dipoles per cubic metre, and how strong each is), and the law is an approximation valid in weak fields. In a strong enough field at low enough temperature, saturation takes over and χ stops meaning anything.
The law itselfgap content
Everything you need from one line
Form 1 — proportionality. χ ∝ 1/T. Double the temperature, halve the susceptibility.
Form 2 — constant product. Since χT = C for the material, two states are linked by χ1T1 = χ2T2. This is the one to use in exams, because you never have to find C.
Form 3 — magnetisation. Combining with M = χH gives M ∝ B/T. Field helps, heat hinders, and they appear on opposite sides of the fraction.
The Curie constant C carries the unit kelvin, because χ is dimensionless and C = χT. Deriving the unit from the equation is always safer than recalling it.
Three rules that turn this into marks
1. Convert to kelvin, every time. A question quoting 27°C and 227°C means 300 K and 500 K. The ratio 300/500 is nothing like 27/227, and this single slip has ruined more answers than the physics ever has.
2. Check the direction before the arithmetic. Cooling must raise χ; heating must lower it. That check alone usually eliminates three of four options.
3. Never compute C unless asked. The constant-product form does the job in one line.
A paramagnetic sample has χ = 4 × 10−4 at 27°C. At 327°C its susceptibility is
How the constant is actually measuredgap content
Why scientists hate curves
Suppose you measure χ at several temperatures and plot it against T. You get a curve. Curves are hard — it is difficult to tell a good curve from a slightly wrong one just by looking.
So do something clever: plot χ against 1/T instead. Because χ = C × (1/T), that turns the law into y = mx — a straight line through the origin. And human eyes are excellent at spotting whether points lie on a straight line.
Better still, the slope of that line is C. You have not just tested the law, you have measured the constant.
Lab 2 · Measure the Curie constant
take readings, fit a linePress Take a reading to measure χ at a random temperature, with a little experimental scatter. The left panel plots χ against T; the right plots the same data against 1/T. Watch which one is easier to judge.
Take three readings and fit; then take ten more and fit again. More data means the scatter averages out and the slope converges on the true constant — which is exactly why real experiments repeat measurements.
The graph question, in both directions
| Plot | Shape for a paramagnet | What the slope means |
|---|---|---|
| χ against T | Falling curve, always above the axis, approaching zero | Not constant — no simple reading |
| χ against 1/T | Straight line through the origin | Slope = C, the Curie constant |
| 1/χ against T | Straight line through the origin | Slope = 1/C |
Exam questions give you one of these three and ask for the shape, or give the shape and ask which is plotted. Read the axis labels before choosing. Both χ-vs-T and χ-vs-1/T appear as options in the same question precisely to catch a hurried reading.
The whole temperature mapgap content
Lab 3 · The phase map
drag the temperatureOne material, the full temperature range. Below the Curie point it is ferromagnetic with a huge susceptibility; above it, the same material follows Curie–Weiss and behaves as a paramagnet.
Drag T down towards TC from above and watch χ blow up. That divergence is the material deciding to magnetise itself without any help — the birth of spontaneous magnetisation.
Real Curie temperatures worth knowing
| Material | Curie temperature | Note |
|---|---|---|
| Cobalt | ≈ 1394 K (1121°C) | The highest of the common ferromagnets |
| Iron | ≈ 1043 K (770°C) | Red-hot iron is no longer magnetic |
| Nickel | ≈ 631 K (358°C) | A hot oven would do it |
| Gadolinium | ≈ 293 K (20°C) | Magnetic in your fridge, not in your hand |
Gadolinium is the memorable one: its Curie point sits at ordinary room temperature, so it is ferromagnetic on a cold day and paramagnetic on a warm one. It is the reason gadolinium appears in NCERT's list of ferromagnetic elements alongside iron, cobalt and nickel.
The Curie–Weiss trap
Above TC the law is χ = C/(T − TC), not C/T. In a ratio problem you must subtract TC first and then treat the two differences as ordinary temperatures.
Worked instance: TC = 300 K, χ = 4 × 10−3 at 400 K, find χ at 500 K. The differences are 100 K and 200 K — a factor of 2 — so χ halves to 2 × 10−3. Using plain Curie's law would have given 3.2 × 10−3, and that wrong answer is always among the options.
Why iron remembersdeleted
Dragging a heavy rug across a rough floor
Push a heavy rug across a floor with splinters and nail heads. It does not glide. It catches, resists, then suddenly jerks forward when you push hard enough. And when you stop pushing, it does not slide back — it stays where the last jerk left it.
Inside a piece of iron, the boundaries between domains — the domain walls — behave exactly like that rug. Impurities, grain boundaries and crystal defects act as the splinters. Walls get pinned.
So when you switch the field off, the walls do not slide back to where they started. Some magnetism stays behind. The iron remembers.
And every jerk wastes a little energy as heat — the same way dragging the rug warms the floor. That waste is the loop area.
Three consequences, all from one cause
Retentivity exists because walls stay pinned when the field is removed. If walls glided freely, B would return to zero and there would be no permanent magnets at all.
Coercivity exists because you must push hard enough in reverse to unpin them again.
Energy loss exists because unpinning is irreversible — the energy spent does not come back. It leaves as heat.
Pinning is why a material is hard or soft. Many defects ⇒ strongly pinned ⇒ hard. Few defects ⇒ walls move freely ⇒ soft. That is genuinely why soft iron is purified and annealed, while permanent magnets are deliberately made from complicated alloys.
Walking the loop, stage by stagedeleted
Lab 4 · The loop walker
the domains, liveLeft is the B–H curve with your position marked. Right shows what the domains inside the material are doing at that exact moment. Step through the full journey and the loop stops being a shape and starts being a story.
Note that the very first climb — from unmagnetised iron up to saturation — happens along a curve that is never travelled again. That is the initial or virgin magnetisation curve, and once you have saturated the sample you cannot get back onto it without demagnetising completely.
| Point | H | B | Name | What the domains are doing |
|---|---|---|---|---|
| O | 0 | 0 | Virgin state | Random directions, cancelling exactly |
| a | +Hmax | +Bs | Saturation | All aligned right; nothing left to align |
| b | 0 | +Br | Retentivity | Mostly still aligned — walls pinned in place |
| c | −Hc | 0 | Coercivity | Half left, half right — net zero, but not random |
| d | −Hmax | −Bs | Reverse saturation | All aligned left |
| e | 0 | −Br | Reverse retentivity | Mostly still aligned left |
| f | +Hc | 0 | Reverse coercivity | Half and half again |
Anchor each term to an axis and you cannot confuse them
Retentivity is the B-axis intercept — the value of B when H = 0. What is retained.
Coercivity is the H-axis intercept — the value of H when B = 0. The coercion needed to erase it.
Point c is subtle and worth pausing on. B = 0 there, but the material is not back to its virgin state. At O the domains were random; at c they are split into two opposing halves that happen to cancel. Same reading, completely different internal condition — which is precisely what "the material remembers" means.
At point c on the loop, B = 0. Compared with the original unmagnetised state at O, the material is
The area is the energydeleted
Why the enclosed area means heat
To change the magnetisation of unit volume by dB, the source must supply work dW = H dB. Over one complete cycle:
If the path retraced itself the outward and return integrals would cancel and the total would be zero. Because the path does not retrace, a non-zero area remains — and that leftover is energy that never comes back. It leaves the material as heat.
Check the units. H is in A m−1 and B is in T. Their product is A m−1 × T = J m−3 — energy per unit volume. The axes themselves tell you the area is an energy density.
In a transformer running at 50 Hz, this loss occurs fifty times a second, continuously, for as long as the device is switched on. Which is why the loop area is not an academic curiosity but a design specification.
A trick worth carrying: area on a graph is almost always energy
Under a force–displacement curve, area is work. Under a pressure–volume curve, area is work. Enclosed by a B–H loop, area is energy lost per cycle per unit volume.
When you meet an unfamiliar graph, multiply the units of the two axes together. If you get joules, or joules per something, the area is an energy.
Design a material for a jobdeleted
Lab 5 · The loop designer
build it, then find its jobSet the coercivity and retentivity yourself and watch the loop reshape. The verdict tells you what your invented material would actually be good for — and what it would be terrible at.
Try the three presets in turn. Note that recording media sit deliberately in the middle — retentive enough to hold data for years, but not so coercive that a write head cannot change it.
| Requirement | Loop shape | Coercivity | Retentivity | Material |
|---|---|---|---|---|
| Transformer core | Narrow, small area | Low | Low–moderate | Soft iron, silicon steel |
| Electromagnet core | Narrow, tall | Low | Low | Soft iron |
| Permanent magnet | Broad, large area | High | High | Alnico, lodestone |
| Magnetic recording | Fairly broad, squarish | Moderate | High | Iron oxide, chromium oxide |
The one-question test
Faced with any application, ask: must this material hold on, or let go?
Hold on ⇒ hard ⇒ broad loop, high coercivity, high retentivity. Permanent magnets, recording media.
Let go ⇒ soft ⇒ narrow loop, low coercivity, small area. Transformers, electromagnets.
Note that "high permeability" and "low retentivity" are not contradictory, though students often reject that combination as impossible. Permeability describes the response while a field is applied; retentivity describes what remains after it is removed. Soft iron has both, and that is exactly why it makes a good electromagnet.
Worked problems
Curie's law ratio · JEE Main 2019 (12 Jan)
350/300 = 7/6 ≈ 1.1667
χ2 ≈ 3.267 × 10−4
Curie–Weiss ratio · typical JEE pattern
T2 − TC = 500 − 300 = 200 K
The difference doubled, so χ halves:
χ2 = 2 × 10−3
Demagnetising current from coercivity · JEE Main 2014
I = Hc/n = 3 × 103/1000 = 3 A
Reading a B–H curve · JEE Main 2020 (7 Jan)
Coercivity = value of H when B = 0 — the horizontal intercept.
Saturation = the maximum value of B, where the curve flattens.
Everything on one page
Six sentences that carry both topics
1. Alignment depends on the ratio of field energy to thermal energy, which is why T ends up in the denominator.
2. χT is a constant, so two states link by simple inverse proportion — and always convert to kelvin first.
3. Plot χ against 1/T to straighten the law; the slope is C.
4. Above the Curie point a ferromagnet obeys Curie–Weiss, and the TC must be subtracted before any ratio.
5. Hysteresis exists because domain walls get pinned on defects — retentivity, coercivity and energy loss all come from that one cause.
6. Loop area is energy lost per cycle per unit volume: narrow for transformers, broad for permanent magnets.
An honest word on priority
Neither of these topics is in your NEET or JEE Main syllabus. Curie's law is at least still set in practice papers and has appeared in past papers, so learning χ = C/T and the ratio method is a sensible half-hour. Hysteresis is deleted from both, and beyond knowing what retentivity, coercivity and loop area mean, further time on it will not pay.
If you are also sitting KCET, MHT-CET, WBJEE, EAMCET or BITSAT, both are live and this page is worth working through properly — particularly Lab 4, since loop-reading questions are common in those papers.
Otherwise: read it once for understanding, do the four worked problems, and put your remaining hours into torque and energy, which carry several times the marks of everything on this page combined.