Curie's Law: Susceptibility vs Temperature Graph

Physics · Magnetism And Matter · NEET

Curie's law says the magnetic susceptibility of a paramagnetic material is inversely proportional to its absolute temperature: χ = C/T, where C is the Curie constant. So a graph of χ against T is a falling curve (hyperbola), while a graph of χ against 1/T is a straight line through the origin with slope C. Memory hook: "Cold Curie" — colder (small T) means bigger χ, so paramagnets are more magnetic when cold.
χ vs T (hyperbola)Tχχ = C/Tχ vs 1/T (straight line)1/Tχslope = Corigin
Left: χ against T is a falling hyperbola (χ = C/T). Right: χ against 1/T is a straight line through the origin with slope equal to the Curie constant C. NEET usually shows the right-hand graph.

Your doubts, answered

Is the Curie's law graph a straight line or a curve?

It depends on the x-axis. χ = C/T. If you plot χ against T (absolute temperature), you get a rectangular hyperbola — a curve that falls as T rises and never touches the axes. If you plot χ against 1/T, you get a straight line passing through the origin with slope equal to the Curie constant C. NEET usually shows the χ-vs-1/T straight line, so read the x-axis label first.

Why does susceptibility decrease when temperature increases in a paramagnet?

A paramagnet has tiny atomic magnets (dipoles) that try to line up with the applied field. Higher temperature means more random thermal motion, which shakes the dipoles out of alignment. So the net magnetisation M for the same field H drops, and since χ = M/H, susceptibility falls. That is why χ is inversely proportional to T.

Does Curie's law apply to diamagnetic materials?

No. Curie's law (χ = C/T) applies only to paramagnetic materials. Diamagnetism comes from induced currents in electron orbits, not from aligning dipoles, so a diamagnet's small negative χ is almost independent of temperature. Do not use χ = C/T for diamagnetic materials in NEET.

What is the difference between Curie's law and Curie temperature?

Curie's law is χ = C/T for paramagnets. Curie temperature (T_c) is a special temperature for ferromagnets: above T_c a ferromagnet loses its strong magnetism and behaves like a paramagnet, following the Curie-Weiss law χ = C/(T − T_c). So Curie's law is about paramagnets; Curie temperature is a threshold for ferromagnets.

⚠️ The NEET trap
Picking the falling hyperbola as the answer when the question plots χ against 1/T.
χ = C/T means χ is a straight line through the origin when plotted against 1/T, and a hyperbola only when plotted against T. Always check the x-axis label (T or 1/T) before choosing.
🧠 Read the axis: T gives a curve, 1/T gives a line.

Real NEET questions

NEET 2023

The variation of magnetic susceptibility (χ) with absolute temperature (T) for a paramagnetic material is best represented by a graph in which:

A · χ vs T is a straight line parallel to the T-axis
B · χ vs 1/T is a straight line passing through the origin
C · χ vs T is a straight line passing through the origin
D · χ vs 1/T is a curve that decreases with 1/T
Solution: Curie's law for a paramagnet: χ = C/T, where C is the Curie constant. Rewrite as χ = C × (1/T). This is of the form y = (slope)(x) with x = 1/T and slope = C, and no constant term. So a plot of χ against 1/T is a straight line through the origin with slope C. A plot of χ against T would instead be a falling hyperbola. Hence the correct representation is χ vs 1/T as a straight line through the origin — option B.

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Frequently asked

What is the Curie constant C?

C is a positive material-dependent constant in Curie's law χ = C/T. It is the slope of the χ-vs-(1/T) straight-line graph. Larger C means a stronger paramagnetic response at a given temperature.

What are the units of susceptibility χ?

Magnetic susceptibility χ is dimensionless (no units) because it is the ratio M/H, and both magnetisation M and magnetic intensity H have the same unit, ampere per metre (A/m).

Is χ positive or negative for a paramagnet in Curie's law?

For a paramagnet χ is small and positive, so C/T is positive and the graph stays in the positive-χ region. Diamagnets have small negative χ and do not follow Curie's law.

What is the Curie-Weiss law?

For a ferromagnet above its Curie temperature T_c, susceptibility follows χ = C/(T − T_c). This is the Curie-Weiss law; it reduces to ordinary Curie's law when T_c is zero.