**Curie Law** is a law in magnetization that establishes a relation between the **magnetic susceptibility **and the **magnetisation** of a paramagnetic material.

A paramagnetic material is a metal that is weakly attracted to magnets.

The relation was experimentally discovered by a French physicist, **Pierre Curie**.

Index

**Statement**

**Statement of Curie Law:** “*The magnetization of a paramagnetic material is directly proportional to an applied magnetic field and inversely proportional to temperature, for large temperatures, weak magnetic fields.*“

**Curie Law ****Formula**

**Formula**

The formula or the equation of Curie’s law is as follows:

\(M = \chi H\), with \(\chi = \frac{C}{T}\)

(After Curie’s temperature, \( \chi = \frac{c^{‘}}{T – T_{C}}\), where \(T_{C}\) is Curie’s temperature and \(c^{‘}\) is a constant)

Where,**? > 0** – Magnetic Susceptibility,**M** – Magnitude of **magnetization**(amperes per meter, A/m),**H** – Magnitude of the applied magnetic field(A/m),**T** – Absolute temperature(kelvins, K),**C** – Material specific Curie constant(k)

The formula or the relation holds only for **high temperatures **or** weak magnetic fields**.

The statement doesn’t hold for all cases.

**Example of Curie Law**

**Question.** A toroid has a mean radius R equal to 20/π cm, and a total of 400 turns of wire carrying a current of 2.0A. An aluminium ring at temperature 280 K inside the toroid provides the core.

(a) If the magnetization I is 4.8×10^{-2} Am^{-1}, find the susceptibility of aluminium at 280 K.

(b) If the temperature of the aluminium ring is raised to 320 K, what will be the magnetization?

**Solution.**

(a) The number of turns per unit length of the toroid is

\(n = \frac{400}{2?R}\)

The magnetic intensity H in the core is

\(H = ni = \frac{400 * 2.0A}{2?*\frac{20}{?}*10^{-2}m} = 2000 A m^{-1}\)

The susceptibility is

\(\chi = I/H\)

\(∴ \chi = \frac{4.8*10^{-2}A m^{-1}}{2000 A m^{-1}} = 2.4*10^{-5}\)

(b) The susceptibility \(\chi\) of a paramagnetic substance varies with absolute temperature as \(\chi = c/T\).

Thus, \(\chi_2/\chi_1 = T_1/T_2\)

The susceptibility of aluminium at temperature 320 K is, therefore,

\(\chi = \frac{280}{320}*2.4*10^{-5} = 2.1*10^{-5}\)

Thus, the magnetization at 320 K is

\(I = \chi H = 2.1*10^{-5}*2000 A m^{-1}\)

\(∴ I = 4.2*10^{-5}Am^{-1}\)

**FAQs**

**What is Curie Law?**Curie law states that the magnetisation of a paramagnetic substance is directly proportional to an applied magnetic field and the susceptibility is inversely proportional to the absolute temperature.

**What is the Curie Temperature?**The temperature at which the magnetic materials lose their permanent magnetic properties is called Curie Temperature.

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