THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Abbe number
V_d = (n_d − 1)/(n_F − n_C), a dimensionless measure of optical dispersion in a material. High V_d (~65) means low dispersion (crown glasses); low V_d (~25) means high dispersion (flint glasses).
Abraham-Lorentz equation
The third-order equation of motion m·a = F_ext + (μ₀q²/6πc)·ȧ for a radiating classical point charge, combining Newton's second law with a jerk-proportional radiation-reaction force. Derived 1903–1904; harbours runaway solutions and acausal pre-acceleration.
AC frequency
The number of full cycles per second of an alternating current or voltage, measured in hertz (Hz). Standard power-grid frequencies are 50 Hz (most of the world) or 60 Hz (North America, parts of South America and Japan).
acceleration
The rate of change of velocity with respect to time; positive when speeding up, negative when slowing down.
Action
The time-integral of the Lagrangian along a trajectory: S = ∫ L dt = ∫ (T − V) dt. Units of energy × time.
Aharonov-Bohm phase
The quantum-mechanical phase Φ = (q/ℏ) ∮ A·dℓ acquired by a charged particle traversing a closed loop, equal to (q/ℏ) times the enclosed magnetic flux. Periodic in the flux quantum Φ_0 = h/|q|; demonstrates that the four-potential is observable in quantum mechanics even where the field is zero.
Ampère's law
The line integral of B around a closed loop equals μ₀ times the enclosed current: ∮ B·dℓ = μ₀ I_enc. Magnetism's analogue of Gauss's law.
Amplitude response
The steady-state amplitude of a driven oscillator as a function of drive frequency — peaked near resonance.
angular acceleration
The rate of change of angular velocity: α = dω/dt; the rotational analogue of linear acceleration.
angular momentum
Rotational analogue of momentum: L = r × p for a particle, L = I·ω for a rigid body; conserved when external torque is zero.
Angular velocity
Rate of rotation, measured in radians per second: ω = dθ/dt. A vector aligned with the rotation axis (right-hand rule).
Anomalous magnetic moment
The deviation of the electron's gyromagnetic ratio from the Dirac value g = 2: a_e ≡ (g − 2)/2 = α/(2π) + O(α²) ≈ 0.00115965218... — the most precisely-tested prediction in physics, agreeing with experiment to 12 decimal places. Schwinger's 1948 calculation was the first triumph of QED.
Antenna gain
The dimensionless ratio G = 4π · (maximum radiation intensity)/(total radiated power) that quantifies how much an antenna concentrates its radiation in its peak direction relative to an isotropic radiator. Usually expressed in dBi (decibels over isotropic).
Antinode
A point on a standing wave where the oscillation reaches its full peak amplitude.
Atmospheric pressure
The weight of the column of air above any point, at sea level ≈ 101.325 kPa or 760 mm Hg.
Back-EMF
The EMF induced in an inductor or motor winding that opposes the change in current or rotation driving it. In a DC motor at steady state, back-EMF roughly equals the supply voltage minus the resistive drop.
Back-reaction
The effect of a radiating charge's own emitted field on its own motion — self-force. Usually small but produces measurable effects like the Abraham–Lorentz radiation-reaction force and the Lamb shift.
Bernoulli's principle
Along a streamline in an incompressible, inviscid fluid, p + ½ρv² + ρgh is conserved.
Bethe-Heitler formula
The 1934 quantum-mechanical bremsstrahlung cross-section derived by Hans Bethe and Walter Heitler, extending Kramers's classical formula to relativistic electrons and thin targets. Full treatment in a later QED branch.
Biot–Savart law
The integral that gives the magnetic field of a steady current: dB = (μ₀/4π) (I dℓ × r̂) / r². Magnetism's analogue of Coulomb's law.
Bound charge
Charge that cannot move freely through a material because it is stuck inside individual atoms or molecules — yet still rearranges locally when the medium is polarized.
Boundary conditions (EM)
The matching rules at an interface between two media: the normal component of D jumps by the free surface charge; the tangential component of E is continuous.
Brewster's angle
θ_B = arctan(n₂/n₁), the angle at which reflected light from a dielectric interface is perfectly s-polarised because the p-polarised Fresnel reflection coefficient r_p vanishes. Brewster 1815.
Buoyancy
The upward force on an object immersed in a fluid, equal to the weight of the fluid the object displaces.
Capacitance
The ratio of charge stored on a conductor (or between two conductors) to the voltage that stored it. C = Q/V. Units: farads.
center of mass
The mass-weighted average position of a system; its motion obeys Newton's laws as if all the mass were concentrated there.
Central force
A force directed along the line connecting two bodies, depending only on their separation. Gravity and Coulomb attraction both qualify.
Centrifugal force
The outward fictitious force that appears in a rotating reference frame, with magnitude Ω²r.
centripetal force
The net inward force that keeps a body moving on a circular path: F_c = m·v²/r = m·ω²·r.
Characteristic impedance
Z₀ = √(L/C) for a lossless transmission line. The ratio of voltage to current in a travelling wave propagating along the line. Standard values: 50 Ω (RF), 75 Ω (video), 100 Ω (differential digital), 377 Ω (free space).