THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Gradient
A vector that points in the direction of steepest increase of a scalar field, with magnitude equal to the rate of that increase.
Grand canonical ensemble
A system free to exchange both energy and particles with a reservoir, at fixed temperature and chemical potential.
gravitational field
The vector field g(r) = −GM/r² r̂ giving the acceleration any test mass would experience at each point in space.
gravity assist
Technique in which a spacecraft gains or loses speed by flying close to a planet, exchanging momentum through the planet's gravitational field.
Group velocity
The speed v_g = dω/dk at which a wave packet's envelope — and therefore its energy and information — propagates.
Group velocity (EM)
v_g = dω/dk. The speed at which a wave packet's envelope — and therefore its energy and information content — propagates. In a dispersive medium v_g differs from the phase velocity v_p = ω/k.
H-field
The auxiliary magnetic field H = B/μ₀ − M, in amperes per metre. Its circulation around a loop is determined by free currents only, ignoring bound currents inside magnetised matter.
Hamilton's equations
The first-order system q̇ = ∂H/∂p, ṗ = −∂H/∂q generating time evolution in phase space.
Hamiltonian
A scalar function H(q, p, t) whose partial derivatives, via Hamilton's equations, generate time evolution. For conservative systems, H = T + V.
Harmonic series
The ladder of integer-multiple frequencies that a bounded system supports above its fundamental.
Heat
Energy transferred between bodies because of a temperature difference — an amount, measured in joules, not a substance.
Heat capacity at constant volume and pressure (C_v, C_p)
A gas has two heat capacities: one at fixed volume and one at fixed pressure, differing by R because expansion does work.
Heat death of the universe
The hypothetical final state in which entropy reaches its maximum and no usable energy gradients remain.
Heat engine
A cyclic device that takes heat from a hot reservoir, turns part of it into work, and rejects the rest to a cold reservoir.
Heat reservoir
An idealised body so large that it can absorb or supply heat without its own temperature changing — the constant-temperature partner of an isothermal process.
Helmholtz free energy
F = U − TS, the work obtainable from a system held at constant temperature and volume.
Hertzian dipole
The idealised point-dipole antenna — an infinitesimally short conductor of length L ≪ λ carrying a uniform oscillating current I(t) = I₀ cos(ωt). Used as the basic radiating element from which the fields of all more complex antennas are built by superposition.
Hohmann transfer
The most fuel-efficient two-burn manoeuvre for moving between two circular orbits; uses a half-ellipse as the transfer path.
Holonomy
The rotation a vector picks up when parallel-transported around a closed loop on a manifold. Vanishes if and only if the curvature is zero. On a 2-sphere of radius R, transporting around a loop enclosing area A rotates the vector by A/R² — the spherical-triangle holonomy reveal that motivates the Riemann tensor.
Hubble constant
The present-day rate of cosmic expansion: the proportionality between a galaxy's distance and its recession velocity.
Huygens's principle
Every point on a wavefront acts as a source of secondary spherical wavelets; the envelope of all the wavelets gives the wavefront at the next instant. Christiaan Huygens, 1678; generalised by Fresnel and Kirchhoff.
Hydrostatic
Relating to fluids at rest. In the hydrostatic limit, pressure varies only with depth: dp/dz = −ρg.
Hysteresis loop
The closed curve traced by B (or M) versus H in a ferromagnet under a cycled applied field. Its enclosed area equals the energy dissipated per unit volume per cycle.
Ideal gas law
PV = nRT — the single equation onto which Boyle, Charles and Avogadro collapse, valid for any gas dilute enough that its molecules barely notice one another.
Image charge
A fictitious charge placed outside the region of interest whose field, together with the real charge's field, satisfies the conductor's boundary conditions.
Impact Parameter
The perpendicular distance from a mass to the undeflected path of a passing ray or particle — the single number that sets how strongly it is bent.
Impedance
Z = V/I for a component or network driven at a single frequency, generalising resistance to the complex plane. Z = R + jX, where R is the resistance (dissipative) and X is the reactance (energy-storing).
impulse
The change in momentum delivered by a force acting over a time interval: J = ∫F dt = Δp.
Incompressible flow
Fluid motion in which density is effectively constant. Liquids, and gases at Mach ≪ 1.
Induced charge
The surface charge that appears on a conductor in response to a nearby external charge, redistributed until the conductor's interior field is zero.