Curie law and Curie temperature
Curie Law and Curie temperature are important topics in IIT JEE. These topics usually fetch direct questions in the exam and so it becomes vital to master them. These topics include various formulae which fetch direct numerical. They are quite easy and don’t require much practice but it is important to clarify these concepts.
The curie law states that in a paramagnetic material, the material’s magnetization is directly proportional to an applied magnetic field. But the case is not the same when the material is heated. When it is heated, the relation is reversed i.e. the magnetization becomes inversely proportional to temperature.
Mathematically, it is written as
M = C x (B / T), where
M is the magnetization
B is the magnetic field, measured in teslas
T is absolute temperature, measured in kelvins
C is a material-specific Curie constant
This concept was initially proposed by French physicist, Pierre Curie and the concept holds good for high temperatures and weak magnetic fields. Various experiments by Pierre Curie showed that for many substances the susceptibility is inversely proportional to the absolute temperature T
χ = C/T.
This relationship is defined as the Curie’s law. The constant ‘C’ is called the curie constant. The above equation may also be modified to χ = C/ (T − θ), where θ is a constant. This equation is called the Curie –Weiss Law which will be discussed later.
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Now we shall discuss some of the important concepts related with this law:
- On increasing temperature, the magnetic susceptibility of paramagnetic materials decreases and vice versa.
- The magnetic susceptibility of ferromagnetic substances does not change according to curie law.
- Curie temperature (TC):
ü The temperature above which a ferromagnetic material behaves like a paramagnetic material is defined as Curie temperature (TC).
ü The minimum temperature at which a ferromagnetic substance is converted into paramagnetic substance is defined as Curie temperature.
ü For various ferromagnetic materials its values are different. e.g. for Ni.
ü At this temperature the ferromagnetism of the substances suddenly vanishes.
Below the Curie point, say 770 degree Celsius, for iron, atoms that act as small magnets align themselves in various magnetic materials. In antiferromagnetic materials, the magnetic fields cancel each other as the atomic magnets alternate in opposite directions. The scenario is quite different in ferromagnetic materials. A fractional reinforcement of magnetic field occurs in them as the impulsive arrangement which is a collection of both patterns, includes two different magnetic atoms.
Curie Weiss Law:
The Curie–Weiss law describes the magnetic susceptibility χ of a ferromagnet in the paramagnetic region above the Curie point.
Mathematically, it is written as
Χ = C/ (T-TC),
Here C is a material specific Curie constant
T is the absolute temperature measured in Kelvin
Tc is the Curie temperature measured in Kelvin.
This law envisages a singularity in the susceptibility at T=Tc. but below this temperature, the magnet will have a spontaneous magnetization.
Remark: In many materials, the Curie-Weiss law fails to describe the susceptibility in the immediate locale of the Curie point.
From the equation as described above
χ = C/ (T − θ), it is clear that when T = θ, the value of the susceptibility becomes infinite. Below this temperature, the material exhibits spontaneous magnetization—i.e., it becomes ferromagnetic. Hence, the magnetic properties of such a material are also quite different from those in the paramagnetic or high-temperature stage. By applying some magnetic field, the magnetic moment can be changed but the amount of moment attained in a given field may vary depending on the last magnetic, thermal or mechanical treatment of the sample.
Other important features and formulae
(i) The horizontal component of earth's magnetic field is from South to North.
(ii) If at any place the angle of dip is θ and magnetic latitude is is λ then,
tan θ = 2 tan λ
(iii) At magnetic equator of earth, λ = 0° and at poles λ = 90°.
(iv) At the poles and equator of earth, the values of total intensity are 0.66 and 0.33 oersted respectively.
(v) In vacuum :– B0 = µ0H
(vi) In medium: – B = µH
(vii) Resultant magnetic field due to I and H :–
(a) B = B1 + BH
= μ0I + μ0H
B = μ0 (I + H)
B = μ0H (1 + I/H)
or B = μ0 (1 + χ)H + = μH
(viii) (a) μ = μ0 [1 + χ]
(b) μ = μ0μ r
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