Curie's Law Calculator

Calculate magnetic susceptibility using Curie's Law and the Curie–Weiss Law for paramagnetic and ferromagnetic materials at any temperature.

About the Curie's Law Calculator

Curie's Law describes how the magnetic susceptibility of paramagnetic materials varies inversely with temperature: χ = C/T, where C is the Curie constant. This simple relationship explains why paramagnets become more responsive to magnetic fields at lower temperatures, as thermal agitation decreases and atomic magnetic moments align more readily with the external field.

The Curie–Weiss Law extends this by incorporating interactions between magnetic moments: χ = C/(T − Tc), where Tc is the Curie temperature. Above Tc, the material behaves paramagnetically. At Tc, susceptibility diverges, signaling the phase transition to ferromagnetic order where spontaneous magnetization appears without an external field.

This calculator implements both Curie's Law and the Curie–Weiss modification, allowing you to compute susceptibility, magnetization, B-field, and relative permeability at any temperature. It generates temperature-dependent susceptibility tables and visual phase diagrams showing the transition between paramagnetic and ferromagnetic regimes. Use this as a practical reminder before finalizing the result.

Why Use This Curie's Law Calculator?

Curie's Law is a cornerstone of magnetism in physics and materials science. This calculator makes it easy to explore temperature-dependent magnetic behavior for research, coursework, and materials characterization without tedious manual calculations. The note above highlights common interpretation risks for this workflow. Use this guidance when comparing outputs across similar calculators. Keep this check aligned with your reporting standard.

How to Use This Calculator

  1. Choose between Curie's Law (ideal paramagnets) or Curie–Weiss Law (real materials with interactions).
  2. Enter the Curie constant C for your material (determines overall susceptibility magnitude).
  3. Input the Curie temperature Tc in Kelvin (the ferromagnetic–paramagnetic transition point).
  4. Set the working temperature T to calculate susceptibility at that specific point.
  5. Enter the applied magnetic field strength H in A/m.
  6. Adjust the number of table points to generate a detailed temperature sweep.
  7. Review the susceptibility chart and regime classification.

Formula

Curie's Law: χ = C / T Curie–Weiss Law: χ = C / (T − Tc) Magnetization: M = χ × H B-field: B = μ₀(H + M) Relative permeability: μr = 1 + χ Where C = Curie constant, T = temperature, Tc = Curie temperature, H = applied field.

Example Calculation

Result: χ ≈ 0.0263, M ≈ 2632 A/m

Using the Curie–Weiss law with C = 1.5 and Tc = 1043 K at T = 1100 K (57 K above Tc), the susceptibility is about 0.0263 and the magnetization in a 100,000 A/m field is approximately 2632 A/m.

Tips & Best Practices

Practical Guidance

Use consistent units, verify assumptions, and document conversion standards for repeatable outcomes.

Common Pitfalls

Most mistakes come from mixed standards, rounding too early, or misread labels. Recheck final values before use. ## Practical Notes

Use this for repeatability, keep assumptions explicit. ## Practical Notes

Track units and conversion paths before applying the result. ## Practical Notes

Use this note as a quick practical validation checkpoint. ## Practical Notes

Keep this guidance aligned to the calculator’s expected inputs. ## Practical Notes

Use as a sanity check against edge-case outputs. ## Practical Notes

Capture likely mistakes before publishing this value. ## Practical Notes

Document expected ranges when sharing results.

Frequently Asked Questions

What is Curie's Law?

Curie's Law states that the magnetic susceptibility of a paramagnetic material is inversely proportional to its absolute temperature: χ = C/T. It was discovered by Pierre Curie in 1895.

When should I use the Curie–Weiss Law instead?

Use the Curie–Weiss Law for real ferromagnetic materials above their Curie temperature, where exchange interactions shift the susceptibility. The Curie–Weiss law is χ = C/(T−Tc) and reduces to Curie's law when Tc = 0.

What is the Curie temperature?

The Curie temperature (Tc) is the critical temperature above which a ferromagnet loses its spontaneous magnetization and becomes paramagnetic. Iron has Tc = 1043 K, nickel 631 K, and cobalt 1394 K.

Why does susceptibility diverge at Tc?

At T = Tc, the denominator (T − Tc) = 0, causing χ → ∞. This mathematically represents the phase transition to ferromagnetic order. In reality, the transition is slightly smoothed by fluctuations.

Can susceptibility be negative?

In diamagnetic materials, χ is negative (typically ~10⁻⁵). Curie's Law applies only to paramagnets with positive χ. Diamagnetism is temperature-independent and not described by Curie's Law.

How do I find the Curie constant experimentally?

Plot 1/χ vs T for paramagnetic data. The slope is 1/C (the reciprocal of the Curie constant). The x-intercept gives the Curie temperature Tc for Curie–Weiss behavior.

Related Pages