Magnetic field

• 1. Introduction

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  The magnetic field is invisible, but a simple compass needle makes its presence unmistakable. Hold one near a wire carrying electric current and the needle swings, pointing in a circle around the wire. That single observation, first demonstrated publicly by Hans Christian Ørsted, overturned centuries of thinking that electricity and magnetism were entirely separate things.

  Magnetic fields surround every magnet, every current-carrying wire, and the Earth itself. They deflect moving electric charges, twist magnets into alignment, attract iron filings into those familiar curved patterns, and even generate new electric currents when they change over time. The questions worth asking are: where do magnetic fields come from, how do they exert force across empty space, and why does a phenomenon discovered through iron needles and compass needles now underpin electric motors, MRI machines, maglev trains, and the entire global electrical power grid?

• 2. Two Fields, One Phenomenon

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  Physicists describe the magnetic field using two closely related but distinct quantities, written as B and H. The B-field, also called magnetic flux density, is the one that directly causes magnetic forces, torques, and electromagnetic induction. Its SI unit is the tesla, symbol T. One tesla equals ten thousand gauss, the unit used in the older Gaussian-cgs system still common in some scientific disciplines.

  The H-field, known as magnetic field strength, is measured in amperes per metre. Inside a vacuum, B and H are equivalent. Inside a material, they diverge because the material's own magnetization contributes to B but not to H. The distinction was first drawn in 1850 by Lord Kelvin, then known as William Thomson, who also coined the term permeability to describe how a given material relates the two.

  The debate over what to call these two fields has persisted for generations among physicists. That debate is primarily about names. The underlying physics is not in question. The international ISO 80000-6 standard formally defines the magnetic field as that component of an electromagnetic field characterized by both B and H, and provides precise definitions for each.

• 3. Force on Moving Charges

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  A charged particle moving through a magnetic field experiences what is known as the Lorentz force, a sideways push perpendicular to both the particle's velocity and the field direction. The force is proportional to the particle's charge, to its speed, and to the component of velocity running perpendicular to the field.

  Because the force is always sideways, it never speeds up or slows down the particle. Instead, a charged particle in a static magnetic field traces a helical path, spinning around field lines while its speed stays constant. The axis of that helix runs parallel to the field.

  When many moving charges flow together as an electric current in a wire, each charge still feels the Lorentz force. The combined effect on the wire is called the Laplace force. Two parallel wires carrying current in the same direction attract each other; reverse one current and they repel. Ampere demonstrated exactly this in the early nineteenth century. A loop of current in a magnetic field does not just get pushed in one direction: the forces on opposite sides of the loop point in opposite directions, producing a net torque that tries to rotate the loop into alignment with the field. That torque is the principle behind every electric motor.

• 4. How Fields Are Created

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  All moving electric charges produce magnetic fields, and the geometry of those fields depends on how the charges are arranged. A straight wire carrying a steady current generates field lines that form concentric circles around the wire. The field strength falls off in inverse proportion to the distance from the wire.

  Bending the wire into a loop concentrates the field inside and weakens it outside. Winding many loops tightly into a coil, called a solenoid, amplifies this effect further. An infinitely long solenoid would have a perfectly uniform field inside and no field at all outside. Wrapping such a coil around an iron core creates an electromagnet: a device that can generate a precisely controlled magnetic field simply by adjusting the current.

  For more complex current arrangements, the Biot-Savart law provides the general calculation tool. It was announced in 1820 by Jean-Baptiste Biot and Felix Savart, though Pierre-Simon Laplace independently derived the underlying differential law and chose not to publish. Ampere's law offers a complementary approach: it relates the total current passing through any loop to the circulation of the H-field around that loop, and is one of the four Maxwell's equations in its modified form accounting for time-varying electric fields.

  The research of magnetic fields as a systematic study began in 1269, when French scholar Petrus Peregrinus de Maricourt mapped the field on the surface of a spherical magnet using iron needles. He named the two points where his field lines converged poles, by analogy to Earth's geographic poles. He also stated that no matter how finely a magnet is sliced, each piece will always have both a north and a south pole.

• 5. Materials and Magnetization

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  Every material responds to an applied magnetic field, though the response varies enormously. Diamagnetic materials produce a weak magnetization opposing the applied field. Paramagnetic materials align weakly in the same direction as the field. Ferromagnetic materials, the class that includes iron and nickel, can maintain a strong magnetization long after the applied field is removed, making them candidates for permanent magnets.

  Closely related are ferrimagnetic and antiferromagnetic materials, which also exhibit magnetization independent of any applied field, though with different internal arrangements. Superconductors represent an extreme case: below a critical temperature and below a lower critical magnetic field, they act as perfect diamagnets, expelling all magnetic flux from their interior. Above those thresholds they enter a mixed state with a complicated and often hysteretic relationship between applied field and internal magnetization.

  At the atomic level, magnetization originates in quantum mechanics. For practical calculations, however, each small volume of a material can be modeled as a tiny current loop with a magnetic dipole moment. The magnetization vector field, M, captures the net dipole moment per unit volume at each point. At distances large enough that the detailed geometry of a magnet no longer matters, any magnetic object can be fully characterized by a single quantity: its magnetic dipole moment. This simplification allows the magnetic fields of atoms to be modeled and extended to describe bulk magnetic materials.

• 6. Electrodynamics and Maxwell

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  In 1831, Michael Faraday discovered that a changing magnetic field generates an encircling electric field, an effect now called electromagnetic induction. This is the operating principle of inductors, transformers, and electrical generators. The governing equation, Faraday's law of induction, relates the voltage induced around a closed loop to the rate of change of magnetic flux through that loop. A companion rule called Lenz's law states that any current induced by a changing field will itself produce a field that opposes the original change.

  Between 1861 and 1865, James Clerk Maxwell unified all of classical electricity and magnetism into a single set of equations. His first paper, On Physical Lines of Force, published in 1861, was valid but incomplete. His 1865 paper, A Dynamical Theory of the Electromagnetic Field, completed the set and demonstrated that light is an electromagnetic wave. Heinrich Hertz experimentally confirmed this in papers published in 1887 and 1888.

  Maxwell's equations also show why changing magnetic and electric fields transmit energy through space. The Poynting vector describes the power flowing per unit area, and its time average, called irradiance, is the quantity used in optics to measure how intense light is at a given point. Albert Einstein's 1905 paper on special relativity revealed that the electric and magnetic fields are not truly separate: what one observer sees as a purely electric force, another observer moving relative to the first will see as partly or entirely magnetic.

• 7. Engineering Applications

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  Nikola Tesla and Galileo Ferraris independently discovered that a rotating magnetic field could drive an electric motor without any mechanical contact between the rotating part and the stationary part. Tesla built an induction motor running on alternating current in 1887. Ferraris published his own research in a paper to the Royal Academy of Sciences in Turin in March 1888, just two months before Tesla received his patent in May 1888.

  The rotating field in a three-phase motor is produced by three coils arranged at mutual angles of 120 degrees, fed with currents of equal magnitude but offset in phase by 120 degrees. The resulting field rotates continuously, and the motor's rotor follows it. The three-phase system's ability to generate a rotating field is a primary reason three-phase power dominates the world's electrical supply systems.

  Beyond motors, magnetic fields are channeled through magnetic circuits, which behave analogously to electrical circuits. Hopkinson's law relates magnetic flux, magnetomotive force, and magnetic reluctance in the same way Ohm's law relates current, voltage, and resistance. This analogy allows engineers to design transformers and other complex magnetic devices using familiar circuit-analysis techniques.

  Magnetic levitation uses magnetic force to suspend an object against gravity with no mechanical support. Applications include maglev trains, magnetic bearings, and contactless melting processes. The largest magnetic field ever produced over a macroscopic volume outside a laboratory was 2.8 kT, achieved at VNIIEF in Sarov, Russia in 1998. Inside a laboratory, researchers at the University of Tokyo produced 1.2 kT over a macroscopic volume in 2018. At the extreme end of the natural world, magnetars hold the record, with fields ranging from 0.1 to 100 GT.

• 8. Earth, Space, and Quantum Limits

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  Earth's magnetic field is generated by convection of liquid iron alloy in the planet's outer core, through a dynamo process in which electric currents and magnetic fields reinforce each other. At the surface, the field resembles what a giant bar magnet tilted about 11 degrees from Earth's rotational axis would produce.

  The field is not static. Its strength varies, its poles drift, and periodically the poles reverse entirely in a process called geomagnetic reversal. The most recent reversal occurred 780,000 years ago. One consequence of the field's existence is the magnetosphere, which shields Earth's ozone layer and the rest of the planet from the solar wind.

  Geologists and archaeologists exploit the field's spatial variations. Aeromagnetic surveys, flown by helicopters, airplanes, and drones, map subtle field variations to locate mineral deposits, chart subsurface geology, and even identify unexploded ordnance. In maritime archaeology, magnetometers reveal wreck sites and identify magnetic materials on the seafloor.

  At the boundary between classical and quantum physics, the electromagnetic field is understood not as a smooth vector quantity but as a quantum field, represented by operators rather than numbers. Quantum electrodynamics, or QED, which is embedded in the Standard Model of particle physics, describes all interactions between charged particles through the exchange of virtual photons. Its predictions agree with experiment to a precision of about one part in ten to the twelfth power, limited by experimental error rather than theory. The classical description given by Maxwell's equations remains accurate for almost every everyday application, but the quantum picture is the deeper one, and the measurement precision benchmark set by Gravity Probe B at 5 attoTesla points toward just how finely the field can be resolved when the instruments are pushed to their limits.