THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Larmor power
The instantaneous total radiated power P = q²a²/(6πε₀c³) of an accelerating point charge, integrated over all solid angle. Synonym of the Larmor formula result; the quantity that appears as the rate of energy loss in radiation-reaction problems.
Length contraction
The relativistic effect that an object of proper length L₀ measured in its rest frame appears contracted to L = L₀/γ along the direction of motion when measured by an observer in any inertial frame moving relative to the object. Symmetric; not a material compression; perpendicular dimensions unchanged.
Lenz's law
The direction of an induced current is always such that its own magnetic field opposes the change in flux that caused the induction. Equivalently: the minus sign in Faraday's law is a consequence of energy conservation.
libration
Bounded oscillation within a potential well, as opposed to full rotation.
Light-cone
The locus of events null-separated from a chosen origin event in spacetime; geometrically a 4D double cone with apex at the origin. The boundary between causally accessible (timelike-interior) and causally inaccessible (spacelike-exterior) regions; the structure that encodes relativistic causality.
Line integral
The integral of a vector field along a curve, measuring the accumulated effect of the field's component tangent to the path.
Linear polarization
An EM wave in which E oscillates along a single fixed line perpendicular to k. Equivalent to a superposition of two circularly polarised waves of equal amplitude with opposite handedness.
Liouville's theorem
Under Hamiltonian flow, phase-space volume is exactly conserved. The foundation of classical statistical mechanics.
Lorentz force
The total electromagnetic force on a point charge: F = q(E + v×B). Bridges Maxwell's macroscopic fields to the motion of individual particles.
Lorentz invariants of the EM field
The two scalar quantities — E·B and |E|² − c²|B|² — that every observer agrees on, regardless of their motion. Constructed as tensor traces from F^{μν}; classify the field as 'electric-like', 'magnetic-like', or 'null'.
Lorentz transformation
The linear coordinate transformation between two inertial frames in special relativity. For a boost along +x at velocity v: t' = γ(t − vx/c²), x' = γ(x − vt), y' = y, z' = z. Replaces the Galilean transformation; reduces to it in the limit β → 0.
Lorentz transformation of fields
The closed-form rule by which the components of E and B transform under a Lorentz boost. Parallel components are unchanged; perpendicular components mix linearly with the perpendicular components of the OTHER field. Derived by Hendrik Lorentz in 1895.
Lorenz gauge
The gauge condition ∇·A + (1/c²)∂V/∂t = 0, which decouples Maxwell's equations for the scalar potential V and vector potential A into two separate wave equations with the same speed c. Named for Ludvig Lorenz (not Hendrik Lorentz).
Luminiferous aether
The hypothetical all-pervasive medium that nineteenth-century physics posited as the substrate in which light waves propagate. Searched for via interferometry from 1881 onward; never detected. Discarded by Einstein's 1905 special-relativity paper.
Lyapunov exponent
The exponential rate λ at which nearby trajectories of a dynamical system diverge. Positive λ means chaos.
Mach number
The ratio of a source's speed to the speed of sound in the surrounding medium.
Magnetic dipole
The smallest possible source of a magnetic field — a tiny current loop or a single particle's intrinsic spin. The magnetic equivalent of an electric dipole.
Magnetic domain
A microscopic region inside a ferromagnet in which all atomic moments point in the same direction. Bulk ferromagnets are partitioned into many such domains, averaging to zero or near-zero net magnetization at rest.
Magnetic energy density
The energy stored per unit volume of a magnetic field: u_B = B²/(2μ₀) in vacuum, u_B = ½ BH in linear matter. The magnetic counterpart of the electric field energy density ε₀E²/2.
Magnetic field
The vector field B that exerts a sideways force on moving charges and steady currents. Sourced by currents and intrinsic spin, never by isolated magnetic charges.
Magnetic moment
The vector m = IA n̂ that quantifies the strength and orientation of a magnetic dipole. Determines its torque, energy, and far-field structure in any external field.
Magnetic monopole
A hypothetical particle carrying isolated magnetic charge g, sourcing the dual field tensor *F^{μν} the way an electron sources F^{μν}. Predicted in 1931 by Dirac as quantum-mechanically consistent; force charge quantisation; arise naturally in grand-unified theories. Never observed despite sixty years of dedicated search.
Magnetic permeability
The factor μ that relates B to H in a linear magnetic material: B = μH. Vacuum has μ = μ₀; other materials are characterised by the relative permeability μ_r = μ/μ₀ = 1 + χ.
Magnetic susceptibility
The dimensionless ratio χ = M/H measuring how strongly a linear magnetic material is magnetised by an applied H-field. Negative for diamagnets, positive and small for paramagnets, large for ferromagnets.
Magnetization
The vector M = (magnetic dipole moment)/(volume) inside a magnetised material, measured in amperes per metre. The magnetic analogue of polarization density.
Malus's law
I = I₀ cos²θ. The transmitted intensity of linearly polarised light through an ideal polariser depends on the cosine-squared of the angle between the incident polarisation and the polariser's transmission axis.
mass
The quantitative measure of a body's inertia; the m in F = ma.
Mass-energy equivalence
Einstein's 1905 result E = mc² — that mass and energy are the same physical quantity expressed in different units, with c² as the conversion factor. Binding energies and kinetic energies register on a balance as mass; the foundation of nuclear physics, fusion, fission, and particle production.
Maxwell stress tensor
T_ij = ε₀(E_iE_j − ½δ_ij E²) + (1/μ₀)(B_iB_j − ½δ_ij B²). The 3×3 symmetric tensor whose divergence gives the mechanical force per unit volume the electromagnetic field exerts on charges and currents.
Maxwell's equations
The four coupled partial differential equations (∇·E = ρ/ε₀, ∇·B = 0, ∇×E = −∂B/∂t, ∇×B = μ₀J + μ₀ε₀ ∂E/∂t) that fully describe classical electromagnetism. Every electromagnetic phenomenon below the quantum scale follows from them.