Magnets: From Fridge Magnets to Levitating Trains

Magnetic field around a magnet — Magnetic field lines around a permanent magnet.
Image source: astronoo.com (new window) — AI-generated image, public domain.

Scientific summary

Astronoo's article explains how magnetism, a force born from the spin of electrons in ferromagnetic materials (iron, cobalt, nickel), makes it possible to go from a small fridge magnet to a levitating train. In these materials, spins spontaneously align to form Weiss domains. When these domains predominantly add up in the same direction, the material becomes a permanent magnet. The scale difference between a small magnet (weak force) and a Maglev train (colossal force) comes down to three factors: the volume of magnetic material (kilometers of rails), the field intensity (superconducting electromagnets or neodymium magnets, several teslas) and the channeling of magnetic flux via soft iron circuits. The same physical force, accumulated on a large scale, makes it possible to make entire trains levitate at over 600 km/h.

How do we go from a small fridge magnet to a levitating train?

Magnetism originates from the spin of electrons, an intrinsic quantum property. In ferromagnetic materials (iron, cobalt, nickel), spins spontaneously align to form Weiss domains. When these domains predominantly add up in the same direction, the material becomes a permanent magnet. The scale difference between a small magnet (weak force) and a Maglev train (colossal force) comes down to three factors: the volume of magnetic material (kilometers of rails), the field intensity (superconducting electromagnets or neodymium magnets, several teslas) and the channeling of magnetic flux via soft iron circuits. The same physical force, accumulated on a large scale, makes it possible to make entire trains levitate at over 600 km/h.

Magnetism: a minor force capable of lifting trains

A fundamental interaction

Magnetism is a manifestation of electromagnetism, one of the four fundamental interactions of nature. It originates from the movement of electric charges and more specifically from the spin of electrons, an intrinsic quantum property, on par with mass or charge.

From small magnets to Maglev trains

At first glance, magnetism seems to be a minor force: a small fridge magnet struggles to hold a few sheets of paper. Yet this same physical force is harnessed by Maglev trains to levitate and guide themselves without contact. An active control system keeps them at an extremely precise distance from the rails (between 10 and 15 mm) without being able to move away or closer. The train is literally "glued" at this height by an intense magnetic field. However, the absence of mechanical friction allows an independent electromagnetic motor to accelerate them to over 600 km/h.

How to go from a negligible force to phenomenal power?

The microscopic origin of magnetism: electron spin

At the most fundamental level, magnetism originates from the spin and electrostatic repulsion of electrons. Each electron behaves like a microscopic bipolar magnet (with a North and South pole). In most materials, these micromagnets (spins) are randomly oriented. Their magnetic effects cancel each other out, so that the material exhibits no net magnetic field at the macroscopic scale.

Ferromagnetic materials and Weiss domains

In ferromagnetic materials (such as iron, cobalt or nickel), electrostatic interactions favor a parallel alignment of electron spins. This alignment of billions of electronic "little compasses" forms microscopic magnetic islands (Weiss domains). Each island is like a large boat with thousands of oarsmen rowing perfectly in the same direction (the spins are aligned). When all the islands predominantly add up in the same direction, the material becomes a very strong permanent magnet.

N.B. :
Weiss domains, named after the French physicist Pierre-Ernest Weiss (1865-1940), are microscopic regions (typically 10 to 100 micrometers) inside a ferromagnetic material where all electron spins are naturally aligned in the same direction, even in the absence of an external field.

The most powerful permanent magnets in the world

This phenomenon of spontaneous alignment is pushed to its peak in certain modern alloys. Rare-earth magnets, such as those composed of neodymium, iron and boron (NdFeB), exploit a particular crystalline structure. This structure strengthens the exchange interaction and "freezes" the alignment of spins, creating materials with extreme properties: record saturation magnetization and resistance to demagnetization. This is what makes NdFeB the most powerful permanent magnet.

Why this scale difference between a fridge magnet and a Maglev train?

The key lies in the difference between spontaneous magnetization and produced magnetic field. In a small fridge magnet, the magnetization (alignment of electron spins) is already strong at the microscopic scale, but the volume of magnetic material is very small and the poles are close, which limits the range and intensity of the field felt at a distance.

In a Maglev train, one does not use a simple permanent magnet of the same size: one uses either superconducting electromagnets (in the electrodynamic system) or a succession of very high-performance permanent magnets (neodymium) associated with active coils. The trick is on the one hand to multiply the active volume (kilometers of rails and entire trains of magnets), and on the other hand to channel and amplify the flux via soft iron magnetic circuits. Above all, in the case of superconducting electromagnets, phenomenal current densities (over 100 A/mm²) are achieved without Joule effect losses, producing magnetic fields of several teslas, thousands of times more intense than that of a small fridge magnet.

Thus, the "minor" force at the gram scale becomes colossal at the ton scale, through accumulation of magnetization, current, and interaction surface.

N.B. :
The first observations of magnetism date back to ancient China, where magnetite was used as early as the 4th century BCE for orientation. In the 19th century, the work of Hans Christian Ørsted (1777-1851) revealed the link between electric current and magnetic field. This discovery was formalized by James Clerk Maxwell (1831-1879), whose equations unify electricity and magnetism.

Magnetism at the heart of 21st century innovations

The table below presents some of the most spectacular applications of modern magnetism, illustrating how this fundamental force is harnessed in fields as varied as transport, medicine, energy or space exploration.

Spectacular applications of modern magnetism
Application field	Technology / Key principle	Impact / Performance	Concrete example
Very high-speed transport	Magnetic levitation (Maglev) & linear motors	Speeds >600 km/h, silence, no mechanical friction	SCMaglev line in Japan (Tokyo-Nagoya), Shanghai Transrapid train
Medical imaging	Magnetic Resonance Imaging (MRI) - Superconducting electromagnets	Magnetic fields of 1.5 to 7 Tesla for non-invasive imaging of soft tissues	Diagnosis of tumors, brain lesions, and muscle pathologies
Nuclear fusion energy	Magnetic confinement of plasma (Tokamak/Stellarator)	Magnetic fields of several Tesla to confine plasma at >100 million °C	International ITER project (France), aiming to demonstrate the feasibility of fusion
Energy storage	Magnetic flywheels on magnetic bearings	Frictionless suspension in vacuum, efficiency >90 %, millisecond response	Stabilization of electrical grids, backup power for data centers
Particle accelerators	Superconducting electromagnets for focusing and deflecting beams	Intense magnetic fields to guide particles at speeds close to that of light	Large Hadron Collider (LHC) at CERN, for fundamental physics research
Environment	High Gradient Magnetic Separation (HGMS)	Extraction of fine metal pollutants or minerals from water and industrial waste	Water treatment, recycling of rare metals, ore purification
Aeronautics & Space	Magneto-plasmadynamic propulsion (MPD) and space protection magnets	High-impulse electric propulsion for long-duration travel; radiation shield	Satellite thrusters; magnetic shield concept for crewed missions to Mars

Historical references of magnetism

The first observations

The first observations of magnetism date back to ancient China, where magnetite was used as early as the 4th century BCE for orientation. The ancient Greeks also knew the properties of the lodestone (magnetite) and its power to attract iron.

The founding discoveries

In the 19th century, the work of Hans Christian Ørsted (1777-1851) revealed the link between electric current and magnetic field. This discovery was formalized by James Clerk Maxwell (1831-1879), whose equations unify electricity and magnetism into a single theory: electromagnetism.

Modern magnetism

The advances of the 20th century have made it possible to understand the microscopic origin of magnetism with quantum mechanics, and to develop materials with extreme magnetic properties, paving the way for the spectacular applications we know today.

References

FAQ: Everything you need to know about magnetization and magnetism

What is the microscopic origin of magnetism?

At the most fundamental level, magnetism originates from the spin of electrons, an intrinsic quantum property on par with mass or charge. Each electron behaves like a bipolar micromagnet with a North and South pole. In most materials, these spins are randomly oriented and their effects cancel out. In ferromagnetic materials (iron, cobalt, nickel), electrostatic interactions favor a parallel alignment of spins, forming microscopic magnetic islands called Weiss domains.

What are Weiss domains?

Named after the French physicist Pierre-Ernest Weiss (1865-1940), Weiss domains are microscopic regions (typically 10 to 100 micrometers) inside a ferromagnetic material where all electron spins are naturally aligned in the same direction, even in the absence of an external field. Each domain is like a magnetic "island" whose spins are perfectly oriented. When these domains predominantly add up in the same direction, the material becomes a permanent magnet.

What are the most powerful permanent magnets and why?

The most powerful permanent magnets are made from rare-earth alloys, such as neodymium-iron-boron (NdFeB). Their particular crystalline structure strengthens the exchange interaction that aligns electron spins and "freezes" this alignment. This gives them record saturation magnetization and resistance to demagnetization. A neodymium magnet can lift several hundred times its own weight. These magnets are used in Maglev trains, electric vehicle motors, wind turbines and computer hard drives.

How does a Maglev train work?

A Maglev train (for Magnetic Levitation) uses magnetism to levitate above the rails, eliminating all mechanical friction. Two main technologies exist: the electrodynamic system (EDS), which uses superconducting electromagnets to produce levitation by magnetic repulsion, and the electromagnetic system (EMS), which uses permanent magnets and coils to keep the train at a constant height by attraction. An active control system keeps the train at a precise distance from the rails (10 to 15 mm), and a linear motor provides propulsion at over 600 km/h.

What is a superconducting electromagnet?

A superconducting electromagnet is an electrical coil made from materials that become superconducting at very low temperatures (generally close to absolute zero, -273.15 °C). In this state, electrical resistance vanishes, allowing very intense currents to circulate without Joule effect losses. This produces extremely powerful magnetic fields, of several teslas, used in Maglev trains, MRIs and particle accelerators.

What are the main applications of magnetism?

Magnetism is used in many fields: magnetic levitation trains (Maglev), magnetic resonance imaging (MRI), plasma confinement in nuclear fusion reactors (tokamaks), energy storage in magnetic flywheels, particle accelerators (such as the LHC at CERN), magnetic separation for depollution and recycling, as well as space propulsion and radiation protection.