B Magnetic FieldEdit

The magnetic field, denoted by B, is a vector field that describes the magnetic influence arising from moving electric charges and from magnetized materials. In the modern framework of electromagnetism, B is as fundamental as the electric field E, and together they form the backbone of how electricity and magnetism interact. In SI units, B is measured in tesla, and its behavior is governed by a set of equations that link electric currents, changing electric fields, and materials with magnetic response. The field is often introduced as part of a larger structure known as electromagnetism and is most succinctly described through Maxwell's equations.

A defining feature of B is that magnetic effects arise from currents and from time-varying electric fields, leading to the familiar picture of magnetic forces acting on moving charges via the Lorentz interaction. The relation F = q(v × B) describes how a charged particle experiences a force perpendicular to both its velocity and the local magnetic field. This makes B central to devices that steer or extract energy from moving charges, and it explains why compasses align with Earth's magnetic field, or why a current-carrying wire generates a surrounding magnetic influence.

B is also characterized by its conservative mathematical structure: in classical electromagnetism, the field has zero divergence (∇·B = 0), which implies that its lines of force form continuous loops with no beginning or end. This contrasts with the electric field, which can originate from charges. The lack of observed magnetic monopoles reinforces the loop nature of magnetic field lines; nevertheless, the theoretical possibility of monopoles remains a topic of inquiry in advanced physics, often discussed in relation to magnetic monopole hypotheses.

In vacua and nonmagnetic media, B is produced by electric currents and by changing electric fields. In steady-state or magnetostatic situations, Ampère’s law (with the displacement current term) and the Biot–Savart law provide practical ways to compute B from current distributions. In time-varying scenarios, Faraday’s law links the evolution of the magnetic field to induced electric fields, illustrating how electricity and magnetism are two faces of a single electromagnetic phenomenon. For a compact formulation of these ideas, see Maxwell's equations.

History

The concept of a magnetic field emerged from the observation that electric currents produce magnetic effects. In the early 19th century, Hans Christian Ørsted discovered that a current through a wire deflects a nearby compass needle, linking electricity to magnetism. André-Marie Ampère quantified the relationship between electric currents and magnetic fields, establishing the network of relationships that would become the core of magnetostatics. Michael Faraday’s experiments showed that a changing magnetic field can induce an electric current, a cornerstone of electromagnetic induction. James Clerk Maxwell later unified these strands into a comprehensive theory, showing that time-varying electric and magnetic fields propagate as electromagnetic waves and that magnetic fields are inseparable from their electric counterparts. Readers may explore Oersted's experiment, Ampère, Faraday's law of induction, and Maxwell's equations for the historical arc that culminated in the modern understanding of the B field.

Fundamentals

Definition and sources: The magnetic field B is produced by moving charges (currents) and by materials with intrinsic magnetic moments. In macroscopic terms, current-carrying wires, coils, and machines generate B; materials with magnetization (the net alignment of microscopic magnetic moments) also contribute to the local B field. See electric current and magnetization for complementary concepts.
Units and measurement: The natural unit of B is the tesla (T). Instruments such as magnetometers and Hall-effect sensors are used to map B in a variety of contexts, from laboratory experiments to geophysical surveys. See tesla and magnetometer.
Fundamental relations: In the language of vector calculus, B is solenoidal, meaning ∇·B = 0, and its curl is related to current and changing electric fields: ∇×B = μ0(J + ε0 ∂E/∂t). In steady situations, the displacement current term vanishes, reducing the relation to Ampère’s law as a practical tool for calculating magnetic fields from currents. See curl and divergence.
Magnetic vector potential: A convenient way to describe B is through a vector potential A, with B = ∇×A. This formulation clarifies gauge freedom and underpins many theoretical approaches in quantum mechanics and field theory. See magnetic vector potential.

Magnetic fields in matter and devices

Relationship to H and M: In matter, B is related to the magnetic field strength H and the magnetization M by B = μ0(H + M). This decomposition helps separate the externally applied field from the material’s own response. See magnetic field and magnetic materials.
Types of magnetic response: Materials can be diamagnetic, paramagnetic, or ferromagnetic, depending on how their atomic moments align in response to an external B field. Ferromagnetic materials, such as iron, can retain a remanent magnetization and enable permanent magnets. See paramagnetism, diamagnetism, and ferromagnetism.
Applications in technology: Magnetic fields are central to a wide range of technologies. Transformers and electric machines rely on magnetic coupling between coils; data storage devices exploit magnetization states; magnetic resonance imaging (MRI) uses strong B fields to interrogate human tissue. See transformer, electric motor, hard disk drive, and magnetic resonance imaging.
Magnetic materials and engineering: The design of magnetic circuits, shielding, and flux concentrating structures is a mature field of engineering. Engineers optimize material properties and geometries to control B for efficient energy conversion and signal processing. See magnetic circuit.

Geophysical and astrophysical contexts

Geomagnetic field: Earth itself hosts a planetary-scale B field generated by dynamo action in the liquid outer core. This field guides navigation and shields the surface from charged particle radiation. See Earth's magnetic field.
Astrophysical magnetism: Magnetic fields pervade the cosmos, from solar and planetary magnetospheres to galactic and intergalactic fields. In many astrophysical settings, magnetic forces influence plasma dynamics and radiation processes, making B a key quantity in space physics. See magnetohydrodynamics.

Observables and related concepts

Magnetic flux and flux density: Magnetic flux through a surface is a measure of how much B penetrates that surface, a quantity central to Faraday’s law and to the operation of devices like inductors. See magnetic flux.
Magnetic moments and dipoles: The B field interacts with magnetic dipoles, both atomic and engineered, leading to alignment phenomena and energy interactions that underlie many sensing and storage technologies. See magnetic dipole.
Gauge and potentials: The description of B via potentials is essential in quantum mechanics, where the vector potential plays a direct role in phase information for charged particles. See vector potential.