About Curie's Law
Curie's law, discovered by French physicist Pierre Curie in 1895, describes how the magnetic response of a paramagnetic material weakens as temperature rises. It states that the volume magnetic susceptibility χ is directly proportional to a material-specific Curie constant C and inversely proportional to the absolute temperature T: χ = C / T. This calculator uses that relationship to find χ, then combines it with an applied field B to find the field intensity H = B / μ₀, the magnetization M = χ × H, and the relative permeability μr = 1 + χ (μ₀ = 4π × 10⁻⁷ T·m/A is the permeability of free space).
Where the formula comes from
In a paramagnetic material, each atom or ion carries a small permanent magnetic moment that points in a random direction because of thermal agitation. Applying an external field B creates a torque that favors alignment with the field, while thermal energy (proportional to kBT) keeps randomizing the orientations. When the magnetic energy per moment is much smaller than the thermal energy — the normal situation for weak-to-moderate lab fields at room temperature — statistical mechanics shows the average magnetization grows linearly with B and falls off as 1/T. Bundling the moment density, the Landé g-factor, the total angular momentum quantum number J, the Bohr magneton, and Boltzmann's constant into one material constant C reproduces χ = C / T.
When Curie's law applies — and when it doesn't
Curie's law is a good approximation for dilute paramagnets (moments far enough apart that they barely interact) at temperatures well above any magnetic ordering transition, and in fields too weak to noticeably align the moments. It breaks down at very low temperature or very high field, where the moments approach full alignment and the magnetization saturates instead of continuing to grow linearly. It also breaks down in materials where neighboring moments interact strongly: those instead follow the Curie-Weiss law, χ = C / (T − θ), where the constant θ shifts the temperature axis to reflect the interactions (θ = 0 recovers pure Curie behavior).