Drawing No. EH–EE–016 // Electrical Engineering

Magnetic Levitation & Diamagnetism Simulator

Reviewed August 2026

Everything that floats magnetically is dodging the same theorem. Change the field, the decay length and the material, and see whether a diamagnet lifts, where it settles, why a permanent magnet cannot be held that way at all, and how a superconductor sidesteps the whole argument.

Educational model. A one-dimensional field decaying as B₀e^−z/L, uniform susceptibility, no demagnetising correction and no field-shape optimisation. It gives the right thresholds and the right scaling; a real magnet array needs a three-dimensional field solution.

Diamagnetic levitation

field gradient against gravity

—

Parameters

Live readout

What to watch for

Size does not appear anywhere

The levitation condition is a balance of force per unit volume, so mass cancels. A gram of graphite and a kilogram of graphite float at the same field. What matters is the material and the field gradient, never the size of the sample.

Susceptibility spans four decades

Pyrolytic graphite is roughly forty times more diamagnetic than water, and threshold field goes with 1/√|χ|, so that is a factor of six. Push the decay length out to the 10 cm of a real bore magnet as well and water passes 10 T — the reason the levitating-frog experiments needed 16 T.

Gradient, not field, does the lifting

A uniform field produces no force at all, however strong. Shortening the decay length raises the gradient and lowers the threshold field, which is why levitation arrays use small magnets in alternating polarity rather than one big one.

The equilibrium is a minimum, and that is the point

On the force tab the curve crosses zero with a negative slope, so a nudge upward gives net downward force and vice versa. That restoring behaviour is exactly what Earnshaw denies to anything attracted towards strong field.

Four escapes from one theorem

The Earnshaw tab lays them out: diamagnets seek a field minimum, superconductors pin flux, spin-stabilised tops use gyroscopic rigidity, and active systems measure and correct. Every levitating device is one of those four.

Pinning works in every direction

A diamagnet is only pushed towards weaker field, so it cannot hang below a magnet. A flux-pinned superconductor is locked to the field pattern and can sit above, below or sideways — and returns to that exact position if displaced.

Sources and technical basis

Susceptibility and density values are reference data; the levitation condition follows from the magnetostatic energy of a linear magnetic material.

OpenStax — University Physics Volume 2Magnetic fields in matter: diamagnetism, paramagnetism and ferromagnetism.NIST — CODATA fundamental constantsVacuum magnetic permeability and standard gravity.NIST — magnetic materials reference dataReference magnetic susceptibility values for the materials offered here.