Curie Constant – Value, Formula, Unit, Limitation

Last Updated : 20 Mar, 2024

Curie Constant represents the proportionality constant in Curie’s law, describing the magnetic susceptibility of a paramagnetic material in relation to temperature. It is denoted by letter “C”. The article discusses the Curie constant, a material-specific constant in Curie’s law, describing its significance, formula, unit, calculation, and applications in magnetic materials.

Table of Content

What is Curie constant
Curie Constant Formula
Curie Law of Magnetism
Curie Constant in Magnetic Materials
Limitations of Curie Constant

What is Curie Constant

Curie constant is a physical constant denoted by the symbol “C.” It is named after the renowned scientist Pierre Curie. It specifically relates to how a material’s magnetic susceptibility changes with temperature. The constant helps scientists understand the behavior of magnetic materials as they undergo temperature variations.

Curie Constant Formula

The formula of curie constant in terms of SI units is given as

$C = \frac {\mu _0 \mu ^2_B}{3k_B} ng^2 J (J+1)$

where,

C is Curie Constant
kB is Boltzmann’s Constant
n is number of atoms per unit volume
μB is Bohr Magnetron
g is Lande-g Factor
μ0 is Permeability of Free Space
J is Angular Momentum Quantum Number

For a two level system, the above equation for curie constant reduces to the following formula

$C = \frac{1}{k_B} n \mu_0 \mu^2$

Since, in magnetic properties, we use SI units and Gaussian units. Hence, in terms of gaussian units, the above formulas are written as below:

$C = \frac {\mu ^2_B}{3k_B} ng^2 J (J+1)$

And for two level system, the above formula is reduced to the following equation

$C = \frac{1}{k_B} n \mu^2$

where, the symbols have same meaning as above and μ is magnetic moment of the material.

Unit and Dimension of Curie Constant

The unit of the Curie constant (C) depends on the unit of magnetic susceptibility (χ) and the unit of temperature (T) in the given system.

The unit of Curie Constant is K.A/(T.m). The other units of Curie Constant is Kelvin per square root of Tesla i.e. KT^-1/2
Dimension of Curie Constant is [M^-1L^-1T²A²K]

Curie Constant Value

The value of the Curie constant depends on the specific material. Different materials have different Curie constants, and they are typically determined experimentally or derived from theoretical models. For example, the Curie constant for iron (Fe) is approximately 1.7 K/T^1/2, while for nickel (Ni), it is around 2.2 K/T^1/2

Properties of Curie Constant

The properties of curie constant is mentioned below:

Material Dependency: The Curie constant varies depending on the specific material being considered. Different materials have different magnetic properties, and their Curie constants reflect these differences.
Curie Temperature Relation: The Curie constant is directly related to the Curie temperature (T_c) of a material. The Curie temperature is the temperature at which a material transitions from a ferromagnetic to a paramagnetic state.
Magnetic Field Sensitivity: The Curie constant indicates the sensitivity of a material’s magnetic properties to changes in the external magnetic field. Higher Curie constants indicate greater sensitivity to magnetic fields.
Magnetic Phase Transition: The Curie constant is associated with the phase transition between ferromagnetic and paramagnetic states in a material.

Curie Law of Magnetism

Curie Law of magnetism states that at temperatures above the Curie temperature (Tc), a ferromagnetic material loses its magnetization and becomes paramagnetic. Below the Curie temperature, the material exhibits ferromagnetic behavior, characterized by spontaneous alignment of magnetic moments within the material.

M = C/(T – T_c)

M is the magnetization
C is Curie Constant
T is the temperature of the material
C is Curie Temperature

The above law can be used to understand the limitations of curie constant.

Curie Constant in Magnetic Materials

It plays a key role in studying how magnetization changes with variations in temperature.
The constant aids scientists in predicting and comprehending the magnetic behavior of materials.
Its significance is particularly notable in the field of magnetic materials, guiding research and applications.
Understanding the Curie constant facilitates the manipulation of magnetic properties for advancements in electronics and materials science.

Curie Constant For Ferromagnetic Material

For ferromagnetic materials, the Curie constant is positive, indicating a positive correlation between temperature and susceptibility.

Curie Constant for Paramagnetic Material

For paramagnetic materials, the magnetic moment is directly proportional to the applied magnetic field and the absolute temperature. Therefore, the Curie constant can be expressed as:

C = x/T

Here, χ is the magnetic susceptibility of the material. The Curie constant is often used to describe the paramagnetic behavior near the Curie temperature (Tc), which is the temperature at which certain materials undergo a phase transition from a paramagnetic to a ferromagnetic or antiferromagnetic state.

Limitations of Curie Constant

The limitations of Curie Constant are mentioned below:

It is different for different materials. Also the curie constant is mostly applicable to ferromagnetic materials and not other type of magnetic materials
Curie Constant is temperature dependent and valid near critical temperature only.
It is sensitive to external factors such as impurities, defects and crystal structure of the material

Curie Temperature

Curie temperature (Tc), named after Pierre Curie, is a critical temperature at which certain materials undergo a phase transition between different magnetic states.

Below the Curie temperature, ferromagnetic and ferrimagnetic materials exhibit spontaneous alignment of magnetic moments, resulting in a net magnetic moment.

Above the Curie temperature, thermal energy disrupts the alignment of magnetic moments, causing them to become randomly oriented. As a result, the material loses its spontaneous magnetization and becomes paramagnetic

Curie–Weiss Law

Curie-Weiss law describes the magnetic behavior of certain materials. It states that the susceptibility of a substance is directly proportional to the difference between its temperature and a specific critical temperature, known as the Curie temperature. This law helps explain the transition from ferromagnetic to paramagnetic behavior in materials.

𝐗 = С∕ T -T_c

Calculation of Curie Constant

Curie constant (C) is a constant that relates the magnetic susceptibility of a material to its Curie temperature. It is given by the Curie-Weiss law:

X=C/T-T_c

where:

χ is the magnetic susceptibility,
C is the Curie constant,
T is the temperature,
T_c is the Curie temperature.

Curie-Weiss law is an empirical relationship that describes the magnetic behavior of certain materials near their Curie temperature. To calculate the Curie constant, you would need experimental data on the magnetic susceptibility (χ), temperature (T), and the Curie temperature (θ).

In practical terms, you could rearrange the equation to solve for C:

C = χ⋅(T−T_c)

So, to calculate the Curie constant, you would need values for magnetic susceptibility, temperature, and the Curie temperature obtained from experimental measurements.

Applications of the Curie Constant

Curie’s law establishes a connection between the magnetization of a material, its temperature, and the applied magnetic field. The law is expressed by the equation:

M = CBT

where:

M is the magnetization of the material
C is the Curie constant
B is the applied magnetic field
T is the temperature on an absolute scale

Considering the relationships M = xH and B = μH, where x is the susceptibility and μ is the permeability, and H is the magnetic intensity vector, we can substitute them into equation (i) to derive a relation between the Curie constant (C) and susceptibility (x):

x = CμT

This derived equation by Pierre Curie underscores that susceptibility and permeability for a paramagnetic material are contingent upon temperature changes.

Curie Constant – PYQ JEE Questions

Q1. A paramagnetic material has 10^28 atoms/m3. Its magnetic susceptibility at temperature 350 K is 2.8 × 10^–4. Its susceptibility at 300 K is

(a) 3.267 × 10^–4

(b) 3.672 × 10^–4

(d) 3.726 × 10^–4

Q2. A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45°, and 40 times per minute where the dip is 30°. If B1 and B2 are, respectively the total magnetic field due to the earth at the two places, then the ratio B1 /B2 is best given by

(a) 0.7

(b) 3.6

(d) 2.2

Q3. A magnetic needle of magnetic moment 6.7 × 10–2 A m2 and moment of inertia 7.5 × 10–6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is

(a) 6.65 s

(b) 8.89 s

(d) 8.76 s

Q4. A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75°. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30° with this field. The magnitude of the other field (in mT) is close to

(a) 1

(b) 11

(d) 1060

Q5. A short bar magnet is placed in the magnetic meridian of the earth with a north pole pointing north. Neutral points are found at a distance of 30 cm from the magnet on the East – West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in Am2 is close to

(a) 9.7

(b) 4.9

(d) 14.6

Q6. Two short bar magnets of length 1 cm each have magnetic moments 1.20 Am2 and 1.00 A m2 respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid-point O of the line joining their centres is close to

(a) 5.80 × 10^–4 Wb/m²

(b) 3.6 × 10^–5 Wb/m²

(d) 3.50 ×10^–4 Wb/m²

Q7. Needles N1, N2 and N3 are made of a ferromagnetic, a paramagnetic, and a diamagnetic substance respectively. A magnet when brought close to them will

(a) attract all three of them

(b) attract N1 and N2 strongly but repel N3

(d) attract N1 strongly but repel N2 and N3 weakly

Q8. A magnetic needle is kept in a non-uniform magnetic field. It experiences

(a) a force and a torque

(b) a force but not a torque

(d) neither a force nor a torque

Q9. The magnetic lines of force inside a bar magnet

(a) are from north-pole to south-pole of the magnet

(b) do not exist

(d) are from south-pole to north-pole of the magnet

Q10. Curie temperature is the temperature above which

(a) a ferromagnetic material becomes paramagnetic

(b) a paramagnetic material becomes diamagnetic

(d) a paramagnetic material becomes ferromagnetic

Curie Constant – FAQs

What is the Meaning of the Curie Constant?

The Curie Constant represents the magnetic susceptibility at the Curie temperature in ferromagnetic materials.

How is the Curie Constant Calculated?

The Curie Constant (C) is calculated using the formula: C = (μ₀ * M²) / (3 * k * T), where μ₀ is the permeability constant, M is magnetization, k is Boltzmann’s constant, and T is temperature.

Who Discovered the Concept of the Curie Constant?

Curie Constant concept was pioneered by Pierre Curie and his wife Marie Curie.

What are the Different Types of Magnetic Constants?

Notable magnetic constants include Curie, magnetic permeability, and susceptibility constants in materials.

When temperature is greater than Curie temperature?

Magnetic materials lose their permanent magnetism above the Curie temperature, undergoing a phase transition and becoming paramagnetic.

What is Curie temperature of pure iron?

The Curie temperature of pure iron is 1043 K (770 °C) when it undergoes a transition from ferromagnetic to paramagnetic state.

What is Curie Formula?

Curie’s law describes the magnetic susceptibility of a material as inversely proportional to the temperature. It is represented as χ = C/T.

What is Curies Constant of Iron?

The Curie constant for iron is approximately 1.68 x 10^-3 K.

How can Curie constant be expressed in Gaussian units?

Curie constant can be expressed in Gaussian units as C = 1.05 x 10^6 emu/(Oe·K).

What is symbol of Curie’s constant?

The symbol for Curie’s constant is ‘C’. It represents the proportionality constant in Curie’s law relating magnetic susceptibility and temperature.

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