Electromagnetism

Electromagnetism is the branch of physics concerned with electric charge, electric and magnetic fields, and their interactions with matter. It unifies electricity and magnetism within a single framework and identifies light as an electromagnetic phenomenon. Classical electromagnetic theory describes fields through Maxwell’s equations and forces through the Lorentz force law; its quantum extension describes electromagnetic interactions in terms of photons. The electromagnetic interaction is one of the four fundamental interactions of nature. (feynmanlectures.caltech.edu)

Historical development

Electric and magnetic phenomena were initially investigated as separate subjects. Their experimental connection became clear in 1820, when Hans Christian Ørsted observed that an electric current deflected a nearby compass needle. André-Marie Ampère subsequently investigated forces between currents, helping establish a quantitative theory of magnetic effects produced by electricity. (aps.org)

In 1831, Michael Faraday discovered electromagnetic induction: changes in magnetic flux can produce an electromotive force. His experiments established principles underlying generators and transformers. Faraday also developed a physical picture in which interactions were associated with fields distributed through space, rather than solely with forces acting directly between distant objects. (rigb.org)

During the 1860s, James Clerk Maxwell combined electrical and magnetic laws into a unified theory. His addition of the displacement-current term made the equations consistent with charge conservation and allowed electromagnetic waves to propagate through empty space. Their predicted speed connected the theory of electricity and magnetism with the previously separate study of light. (feynmanlectures.caltech.edu)

Charges, fields, and forces

An electric field, conventionally denoted E, specifies the electric force per unit positive test charge. A magnetic field, denoted B, contributes a force on moving charges. The combined force on a point charge $q$, moving with velocity $\mathbf{v}$, is expressed by the Lorentz force law:

The magnetic contribution is perpendicular to the charge’s velocity. Consequently, it changes the direction of motion but does no work on that point charge by itself; an electric field can change its kinetic energy. (feynmanlectures.caltech.edu)

Coulomb’s law describes the electrostatic force between stationary point charges: like charges repel, unlike charges attract, and the force magnitude decreases with the square of separation. Fields provide a local description of these interactions, assigning physical quantities to positions in space. Electric currents produce magnetic fields, while changing magnetic fields produce circulating electric fields. (feynmanlectures.caltech.edu)

Maxwell’s equations

Maxwell’s equations comprise four relationships governing classical electromagnetic fields. In microscopic form, using SI units, they are

Here $\rho$ is charge density, $\mathbf{J}$ is current density, and $\varepsilon_0$ and $\mu_0$ are vacuum permittivity and permeability. The equations relate field divergence to sources and field circulation to currents or time-dependent fields. (feynmanlectures.caltech.edu)

The first equation is Gauss’s law for electricity. The second states that magnetic flux through a closed surface vanishes in the standard theory. The third expresses Faraday’s induction law, and the fourth is the Ampère–Maxwell law. Their differential and integral forms describe the same relationships at different spatial scales. Combined with the force law, material properties, and appropriate initial and boundary conditions, they determine classical electromagnetic behavior. (feynmanlectures.caltech.edu)

Radiation, energy, and relativity

In vacuum, Maxwell’s equations admit traveling-wave solutions whose propagation speed is

This is the speed of light. For a plane wave in vacuum, the electric and magnetic fields are mutually perpendicular and perpendicular to the propagation direction. Electromagnetic radiation includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, distinguished by frequency and wavelength. Their common field description connects electromagnetism with optics. (feynmanlectures.caltech.edu)

Fields carry energy and momentum. In vacuum, their energy density is

and energy flow is represented by the Poynting vector, $\mathbf{S}=\mathbf{E}\times\mathbf{B}/\mu_0$. Field momentum accounts for effects such as radiation pressure and is necessary for a complete description of conservation laws involving matter and radiation. (feynmanlectures.caltech.edu)

Electric and magnetic fields are not independent entities under the theory of relativity. Observers moving relative to one another generally assign different electric and magnetic components to the same electromagnetic field. Maxwell’s equations retain their form under the Lorentz transformations connecting inertial reference frames. (ocw.mit.edu)

Matter, quantum theory, and applications

Materials respond to fields through charge motion, electric polarization, and magnetization. In a dielectric, an applied electric field displaces bound positive and negative charges or reorients molecular dipoles. Macroscopic descriptions average over microscopic structure and introduce material parameters; these parameters need not be constant or identical in every direction. (feynmanlectures.caltech.edu)

At microscopic scales, quantum mechanics is required. Quantum electrodynamics describes the quantum electromagnetic field and its interactions with charged particles; the photon is its force carrier. Within the Standard Model, electromagnetic and weak interactions belong to the unified electroweak interaction. Gravity is not included in that model. (home.web.cern.ch)

Practical uses follow directly from field behavior. An electric generator converts mechanical input into electrical output through induction, while an electric motor uses electromagnetic forces to produce motion. Transformers transfer energy between circuits through changing magnetic flux. Transmitting and receiving electromagnetic waves provides the physical basis of radio communication, while dielectric materials control field storage and distribution in capacitors. (rigb.org)