THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Electromagnetic duality
The symmetry E → cB, cB → −E (equivalently F^{μν} → *F^{μν}) that maps the source-free Maxwell equations to themselves. In a universe with magnetic monopoles, the duality extends to interchanging electric and magnetic charges/currents, restoring perfect E↔B symmetry to the field equations.
Electromagnetic field
The unified field consisting of both the electric field E and the magnetic field B (equivalently, the antisymmetric tensor F^μν). Classical electromagnetism is the study of its dynamics. Full treatment across §07–§08.
Electromagnetic field tensor
The rank-2 antisymmetric 4×4 tensor F^{μν} that packages the three components of E and three components of B into one Lorentz-covariant object, with F^{0i} = E_i/c and F^{ij} = -ε_{ijk} B_k. Also called the Faraday tensor.
Electromagnetic induction
The generation of an electromotive force in a circuit whenever the magnetic flux through it changes. Discovered by Faraday and Henry in 1831, it is the foundation of every electric generator, transformer, and inductive sensor ever built.
Electromagnetic spectrum
The full range of frequencies (or equivalently wavelengths) of EM radiation, from kilohertz radio to zettahertz gamma rays. All regions are the same physical phenomenon — classical EM waves — differing only in ω.
Electromagnetic wave
A self-sustaining coupled oscillation of electric and magnetic fields that propagates through vacuum at c = 1/√(μ₀ε₀). E, B, and k are mutually perpendicular. Maxwell's synthesis identified light itself as an electromagnetic wave.
Electromagnetic wave equation
The second-order PDE ∇²E = (1/c²)∂²E/∂t² (and identically for B), derived from Maxwell's equations in source-free vacuum. Its plane-wave solutions propagate at c = 1/√(μ₀ε₀).
Electromotive force (EMF)
The work per unit charge done by a source on charges as they move around a closed circuit, measured in volts. Despite the name, EMF is not a force; it is the energy-per-charge a battery, generator, or induction process supplies.
ellipse
Closed curve where the sum of distances from any point to two foci is constant.
elliptic integral
Integral involving square root of cubic/quartic polynomial; gives the exact period of a large-angle pendulum.
Elliptical polarization
The general polarisation state of a single-frequency EM wave: the E-vector traces an ellipse per cycle. Linear and circular polarisations are the two degenerate limits.
EM Lagrangian density
The Lorentz-invariant scalar L = −¼F_{μν}F^{μν} − A_μJ^μ from which all of classical electromagnetism follows. Euler-Lagrange recovers Maxwell's equations; gauge invariance via Noether gives charge conservation. The cleanest sentence in physics.
Energy cascade
Richardson's picture: energy injected at large scales is handed down, eddy by eddy, to smaller scales until viscosity dissipates it as heat.
epicycle
Small circle whose center moves along a larger one; Ptolemy's device for saving uniform circular motion.
equatorial bulge
The excess of the Earth's equatorial radius over its polar radius (about 21 km), caused by the centrifugal deformation of rotation.
Equipotential
A surface on which the electric potential is constant. No work is done moving a charge along an equipotential, and the electric field is everywhere perpendicular to it.
escape velocity
The minimum speed needed to escape a gravitational field: v_esc = √(2GM/r). For Earth's surface, ~11.2 km/s.
Euler angles
Three angles specifying the orientation of a rigid body in space relative to a fixed reference frame.
Euler-Lagrange equations
d/dt(∂L/∂q̇) = ∂L/∂q — the differential form of stationary action, equivalent to Newton's second law.
Far-field zone
The region r ≫ λ surrounding an oscillating source where the field is an outgoing spherical wave with amplitude ∝ 1/r and time-averaged Poynting flux that transports energy irreversibly outward. Also called the radiation zone, Fraunhofer zone, or wave zone.
Farad
The SI unit of capacitance. One farad holds one coulomb of charge per volt of potential difference. Symbol: F.
Faraday cage
A conducting enclosure that blocks external static and low-frequency electric fields by redistributing charge on its surface.
Faraday's law
EMF = −dΦ_B/dt. The induced electromotive force in a closed loop equals the negative rate of change of magnetic flux through the loop. The first of Maxwell's time-dependent equations.
Fermat's principle
Light travels between two points along the path that takes the least time.
Ferroelectricity
The presence of a spontaneous electric polarization in certain crystals that can be reversed by an applied field — the electric analogue of ferromagnetism.
Ferromagnetism
The spontaneous parallel alignment of atomic magnetic moments via quantum exchange interaction, producing permanent magnetization below a critical Curie temperature. The origin of magnetism in iron, nickel, cobalt, and everyday magnets.
Field energy density
The energy stored per unit volume in an electric field: u = ½ε₀E². Measured in joules per cubic metre.
Field line
A curve whose tangent at every point is the direction of the electric field there. Lines begin on positive charges and end on negative ones.
Field momentum
g = ε₀ E×B = S/c². The momentum density carried by the electromagnetic field. Integrated over a volume, it gives the total mechanical momentum the field carries, separate from the momentum of charges and currents.
Flux
A scalar measure of how much of a vector field passes through a surface, weighted by the field's component normal to the surface.