Calculate the Curie constant for paramagnetic materials by entering the number of magnetic moments per unit volume (N/V) and the magnetic moment (μ). You can also compute magnetization (M) by providing the magnetic field (B) and temperature (T). Results include the Curie constant (C), magnetization (M), and magnetic susceptibility (χ).
Curie Constant (C)
--
Magnetization (M)
--
Magnetic Susceptibility (χ)
--
Curie Constant per Mole (Cm)
--
The Curie constant (C) characterizes the magnetic susceptibility of a paramagnetic material. It quantifies how strongly the material responds to an applied magnetic field. A larger Curie constant means the material magnetizes more easily per unit of applied field and temperature.
Curie's law states that the magnetization M of a paramagnetic material is directly proportional to the applied magnetic field B and the Curie constant C, and inversely proportional to the absolute temperature T. The equation is M = (C / T) × B. This means at lower temperatures, the same field produces stronger magnetization.
The Curie constant is given by C = (μ₀ / 3k_B) × (N/V) × μ², where μ₀ is the permeability of free space (4π×10⁻⁷ T·m/A), k_B is Boltzmann's constant (1.381×10⁻²³ J/K), N/V is the number density of magnetic moments, and μ is the magnetic moment of each atom.
Paramagnetic materials are substances that are weakly attracted to external magnetic fields. They contain unpaired electrons that act as tiny magnetic dipoles. When placed in a magnetic field, these dipoles partially align with the field, creating a net magnetization. Examples include aluminum, platinum, and oxygen gas.
Magnetic susceptibility (χ) measures how much a material becomes magnetized in response to an applied magnetic field, defined as χ = M / H ≈ μ₀M / B. For paramagnets following Curie's law, χ = C / T, meaning susceptibility decreases as temperature rises — the thermal agitation disrupts magnetic alignment.
The Bohr magneton (μ_B ≈ 9.274×10⁻²⁴ J/T) is the natural unit of magnetic moment for electrons. Most paramagnetic atoms have magnetic moments that are integer or half-integer multiples of the Bohr magneton, making it the standard reference value in calculations involving atomic magnetism.
At higher temperatures, thermal energy (k_B × T) increasingly randomizes the orientation of atomic magnetic dipoles, counteracting alignment with the external field. Since M = C × B / T, the magnetization is inversely proportional to temperature — a fundamental consequence of Curie's law.
The Curie constant C describes how a paramagnetic material responds to a magnetic field at a given temperature. The Curie temperature (T_C), on the other hand, is the critical temperature above which a ferromagnetic material loses its spontaneous magnetization and becomes paramagnetic. They are related concepts but apply to different regimes of magnetic behavior.