THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Displacement current
The term ε₀ ∂E/∂t Maxwell added to Ampère's law in 1861 to restore consistency with charge conservation. A changing electric field produces a magnetic field just as a current does — and the term makes Maxwell's equations predict light.
Displacement field
The vector D = ε₀E + P whose divergence equals only the free charge density. Lets you do Gauss's law inside a dielectric without tracking bound charges.
Divergence
A scalar measure of how much a vector field spreads outward from a point, per unit volume. ∇·F = source density.
drag
Resistive force exerted on a body moving through a fluid; linear in velocity at low speeds, quadratic at high speeds.
Dual field tensor
The Hodge dual *F^{μν} = (1/2) ε^{μνρσ} F_{ρσ} of the electromagnetic field tensor, obtained by swapping E and cB (up to signs in mostly-minus signature). Sources magnetic monopoles in the symmetric Maxwell equations; never observed sourced.
Duane-Hunt limit
The sharp high-energy cutoff of the bremsstrahlung X-ray spectrum at E_max = eU, where U is the accelerating voltage of the tube. Discovered by William Duane and Franklin Hunt at Harvard in 1915 and one of the early confirmations that E = hν.
eccentricity
Dimensionless number between 0 and 1 describing how squished an ellipse is.
Einstein equivalence principle
The form of the equivalence principle Einstein needed for general relativity: WEP + local Lorentz invariance + local position invariance. Inside any sufficiently small freely falling laboratory, the laws of physics reduce to special relativity, and any deviation would be measurable by a sensitive enough experiment.
Einstein field equations
G_{μν} = (8πG/c⁴) T_{μν}. Ten coupled nonlinear partial differential equations relating spacetime geometry (left) to matter-energy distribution (right). The defining equations of general relativity. Published November 1915 by Einstein; near-simultaneously derived by Hilbert via the Einstein-Hilbert action.
Einstein tensor
G_{μν} = R_{μν} − (1/2) R g_{μν}. The unique divergence-free combination of Ricci and metric — ∇^μ G_{μν} = 0, a consequence of the contracted Bianchi identities. The geometric side of Einstein's field equations G_{μν} = (8πG/c⁴) T_{μν}.
elastic collision
A collision in which total kinetic energy is conserved as well as total momentum.
Electric charge
The fundamental conserved quantity that produces electric forces. Comes in ± signs. Measured in coulombs.
Electric field
The force per unit charge that a test charge would feel at a given point. A vector field filling all of space. Units: newtons per coulomb, equivalently volts per metre.
Electric potential
The electrostatic potential energy per unit charge at a point. A scalar field measured in volts. V = −∫E·dℓ from a reference point.
Electric susceptibility
The dimensionless coefficient χ_e in P = ε₀χ_e E that measures how easily a dielectric polarizes in response to an applied electric field.
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 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 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.
Eötvös parameter
The dimensionless ratio η = (m_g − m_i)/m_i quantifying the fractional difference between gravitational and inertial mass for a given material. Eötvös's torsion-balance experiments constrained η ≲ 10⁻⁹; modern Eöt-Wash and MICROSCOPE measurements push the bound to ≲ 10⁻¹⁵.
epicycle
Small circle whose center moves along a larger one; Ptolemy's device for saving uniform circular motion.
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.
Equivalence principle
Einstein's foundational GR axiom: no local experiment can distinguish a freely falling laboratory in a gravitational field from an inertial laboratory in flat spacetime. Comes in three increasingly strong forms — weak (m_g = m_i), Einstein (WEP + local Lorentz invariance + local position invariance), and strong (extends to self-gravitating bodies).
escape velocity
The minimum speed needed to escape a gravitational field: v_esc = √(2GM/r). For Earth's surface, ~11.2 km/s.