Q.What is Curie law?

Curie's Law: Why Heat Kills Magnetism

Imagine a room full of tiny compass needles, each free to spin. At room temperature, they jostle around randomly — point every which way, and the net direction is zero. Now walk in carrying a strong bar magnet. The needles feel the tug and try to align with your magnet's field. But thermal jostling fights back, shaking them loose. The stronger the shaking (higher temperature), the harder it is to keep them lined up.

That tug-of-war is the heart of paramagnetism.

The Intuition

A paramagnetic material has atoms with permanent magnetic moments — think of each atom as a tiny bar magnet. Without an external field, thermal energy randomises their directions; net magnetisation is zero. Apply a magnetic field $B$, and each moment wants to align with $B$ (lower energy). But temperature $T$ supplies random kicks that knock them out of alignment.

Two competing effects:

• Field tries to align them → magnetisation $M$ grows with $B$.
• Temperature tries to randomise them → $M$ shrinks as $T$ rises.

The simplest guess? Magnetisation should be proportional to $B/T$. That guess is exactly Curie's Law.

The Precise Statement

For a paramagnetic material in a not-too-strong magnetic field, the magnetisation $M$ (magnetic moment per unit volume) is

where $C$ is the Curie constant (depends on the material — number of magnetic atoms per volume and their individual moment strength). The magnetic susceptibility $\chi$ is defined by $M = \chi B$, so

This is Curie's Law: susceptibility is inversely proportional to absolute temperature. Double the temperature, halve the susceptibility.

What It Tells You

• At high $T$: thermal chaos wins — the material barely responds to a field ($\chi$ small).
• At low $T$: alignment becomes easier — $\chi$ grows large.
• It fails when $B$ is very strong or $T$ is very low (then all moments are nearly aligned, and you can't get more magnetisation — saturation). It also fails if the material orders magnetically (ferromagnetism, antiferromagnetism) below some critical temperature.

Why It Works (Briefly) …