Magnetic field

A magnetic field is a physical field that exerts influence on moving electric charges, electric currents, and magnetic materials. It is a fundamental component of electromagnetism and one of the essential interactions governing physical processes in nature. Magnetic fields arise from both electric currents and the intrinsic magnetic moments of elementary particles, which are associated with their quantum mechanical spin. They play a central role in technology, geophysics, astrophysics, and engineering.

Fundamental Description and Properties

Magnetic fields affect charged particles by exerting a force that is always perpendicular to both the particle’s velocity and the direction of the field. This phenomenon is described by the Lorentz force law, which states that a charged particle experiences a magnetic force proportional to its charge, velocity, and the magnetic flux density at its location. Because the force depends on motion, stationary charges are unaffected by magnetic fields alone.
Magnetic fields are represented mathematically as vector fields, assigning a directional vector to each point in space. They are often considered pseudovector fields because they behave differently under certain coordinate transformations. In physics and engineering, two closely related quantities are used:

• B-field (magnetic flux density or magnetic induction)
• H-field (magnetic field strength or magnetising field)

These fields differ in how they account for the presence and response of materials. In a vacuum, they are directly proportional through the vacuum permeability. In materials, however, magnetisation modifies the local relationship between the two.
The SI unit for magnetic flux density B is the tesla (T), whereas field strength H is measured in amperes per metre (A/m). Magnetic flux itself is measured in webers, closely related to the tesla.

Origins of Magnetic Fields

Magnetic fields arise from two main physical sources:

• Moving electric charges, producing magnetic fields around current-carrying conductors.
• Intrinsic magnetic moments of particles, resulting from spin, a fundamental quantum property.

These origins combine to generate complex patterns such as those found in permanent magnets, electromagnets, and planetary magnetic fields.
Electromagnetism links electric and magnetic fields, showing that time-varying electric fields also generate magnetic fields. This interdependence forms the basis of electromagnetic waves and many technological applications.

Magnetic Forces and the Lorentz Law

The Lorentz force law defines the magnetic component of the force on a charged particle. The relationship incorporates the cross product of the particle’s velocity and the magnetic flux density, ensuring that the force is always perpendicular to motion. The magnitude of the magnetic force is proportional to the charge, the speed, the field strength, and the sine of the angle between velocity and field direction.
To determine the direction of the force, the right-hand rule is used: the thumb points along the current or velocity, the fingers in the direction of the magnetic field, and the force emerges from the palm. Negatively charged particles experience the opposite direction of force to that indicated by the rule.
Magnetic forces also act on magnetic dipoles, producing torques that align dipoles with the field. This behaviour is crucial in devices such as compasses and in the orientation of atomic-scale magnetic domains.

Magnetic Materials and Responses

Different materials respond to magnetic fields in characteristic ways:

• Ferromagnetic materials, such as iron, experience strong attraction due to alignment of internal magnetic domains.
• Paramagnetic materials experience weak attraction because unpaired electrons align slightly with the field.
• Diamagnetic materials are weakly repelled because induced currents oppose the field.
• Antiferromagnetic materials possess ordered but opposing magnetic moments that cancel macroscopically.

Ferromagnetism is the strongest of these responses and is responsible for permanent magnets and many industrial applications.

Technological and Scientific Applications

Magnetic fields underpin numerous modern technologies. Rotating magnetic fields are essential in electric motors and generators, enabling the conversion between electrical and mechanical energy. In transformers, magnetic circuits describe how fields interact with coils and magnetic cores to alter voltage and current characteristics.
Magnetic fields inside electrical devices allow analysis of charge carriers through the Hall effect, which is used to measure magnetic fields, detect current, and characterise materials.
In geophysics, the Earth’s magnetic field shields the planet from charged particles in the solar wind. This field supports navigation by providing directional reference for compasses and exhibits long-term variations and periodic polarity reversals. In space science, magnetic fields structure charged particle motions around planets, stars, and galaxies.

Mathematical Representation of B and H Fields

The B-field describes the magnetic effect that directly influences the motion of charged particles. It is defined so that it correctly predicts the magnetic force in the Lorentz law. The H-field, however, incorporates information about magnetisation and is used to simplify calculations involving magnetic materials.
Their relationship is expressed as:
B = μ₀(H + M)
where μ₀ is the vacuum permeability and M is the magnetisation of the material. In vacuum, magnetisation is zero, making the two fields directly proportional.
Both fields are recognised as magnetic fields in many contexts, though naming conventions differ among scientific disciplines and textbooks.

Measurement of Magnetic Fields

Devices that detect and quantify magnetic fields are known as magnetometers. Several types exist:

• Search-coil magnetometers, sensitive to changes in magnetic fields.
• Hall-effect magnetometers, using voltage differences produced by magnetic influence on charge carriers.
• Fluxgate magnetometers, widely used in aerospace and geophysics.
• SQUIDs (superconducting quantum interference devices), offering extremely high sensitivity.
• Proton magnetometers, which measure precession frequencies of hydrogen nuclei.