THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Polarization
The alignment of bound charges inside a dielectric — every atom or molecule turns into a tiny dipole that points along the local electric field.
Polarization axis
For a linearly polarised wave, the direction along which E oscillates. For a polariser, the transmission axis along which the incident E-component is passed. Set by the vector structure of the wave, not its scalar amplitude.
Polarization density
The vector P = (dipole moment)/(volume), measured in coulombs per square metre, that summarises how strongly a dielectric is polarized at each point.
potential energy
Energy stored in the configuration of a system against a conservative force, retrievable by reversing that configuration.
potential well
Region of potential energy that traps a system; shape determines oscillation character.
power
The rate at which work is done or energy is transferred: P = dW/dt, measured in watts (J/s).
Poynting vector
S = (1/μ₀)·E×B. The vector whose magnitude gives the energy-flux density (W/m²) of the electromagnetic field and whose direction gives the flow direction. Introduced by Poynting in 1884.
Poynting's theorem
∂u/∂t + ∇·S = −J·E. The local statement of energy conservation for the electromagnetic field: rate of change of field-energy density plus divergence of energy flux equals the negative of work done by fields on charges.
Pressure
Force per unit area acting perpendicular to a surface. Scalar. Unit: pascal (Pa = N/m²).
principal axes
Three mutually perpendicular body-fixed axes about which the inertia tensor is diagonal; spinning about them produces no wobble.
Principle of least action
Of all paths a system could take between two fixed events, the one realised in nature is the path for which the action S is stationary.
Proper time
The time τ measured by a clock carried along a particle's world-line. Related to coordinate time by dτ = dt/γ, so dτ = √(1 − β²) dt; integrated along a timelike world-line gives the arc length in the Minkowski metric. Lorentz-invariant; the geometric content of time dilation.
quality factor
Quality factor Q = ω₀/γ; number of oscillations before energy drops to 1/e.
Quality factor (Q)
Dimensionless number Q = ω₀L/R = 1/(ω₀RC) = (1/R)·√(L/C) for an RLC circuit, measuring how sharply resonant the response is. Equivalently Q = 2π · (energy stored) / (energy lost per cycle).
Radiation pattern
The angular distribution of an antenna's far-field radiated power as a function of direction, dP/dΩ(θ, φ). For a short dipole the pattern is the sin²θ doughnut; for arrays and apertures it is the magnitude-squared Fourier transform of the current distribution.
radius of gyration
The distance k = √(I/M) at which a point mass equal to the body's total mass would have the same moment of inertia.
range
Horizontal distance covered by a projectile before it returns to its launch height; maximised at 45° in vacuum.
RC time constant
τ = RC. The characteristic time for an RC circuit to charge to 1−1/e ≈ 63% of its final voltage, or discharge to 1/e ≈ 37% of its initial voltage. In seconds when R is in ohms and C in farads.
Reactance
The imaginary part X of impedance Z = R + jX. Inductive reactance X_L = ωL is positive; capacitive reactance X_C = −1/(ωC) is negative. Reactance stores energy without dissipating it.
Refractive index
The ratio n = c/v_p of the vacuum speed of light to the phase velocity in the medium.
Relativistic velocity addition
The rule for combining velocities in special relativity. For collinear motion: u' = (u − v)/(1 − uv/c²). Replaces the Galilean rule u' = u − v; ensures no combination of subluminal velocities exceeds c.
Relativity of simultaneity
The result that two spatially-separated events judged simultaneous in one inertial frame are not simultaneous in any other frame moving relative to the first. The deepest break with Newtonian intuition; the geometric content of the Lorentz transformation's time-mixing.
Resistance
The ratio R = V/I for a conductor obeying Ohm's law. Measured in ohms (Ω). Determined by the conductor's geometry (R = ρℓ/A) and material resistivity ρ.
Rest energy
The energy E₀ = mc² that a massive particle has in its own rest frame, where its three-momentum vanishes and its four-momentum reduces to (mc, 0, 0, 0). The conversion factor between mass and energy; the floor below which a particle's total energy cannot drop.
restoring force
Force proportional to displacement and directed back toward equilibrium: F = −kx.
Retarded time
The earlier time t_r = t − |r − r_s(t_r)|/c at which a signal must have left a moving source in order to arrive at the observer at time t. Built into the retarded potentials and all causal electromagnetic radiation formulae.
Reynolds number
Dimensionless ratio Re = ρvL/η of inertial to viscous forces. Re ≪ 1: creeping flow. Re ≫ 1: turbulent.
RL time constant
τ = L/R. The characteristic time for current in an RL circuit to rise to 1−1/e ≈ 63% of its steady-state value, or decay to 1/e ≈ 37% of its initial value.
Roche limit
The minimum orbital distance at which tidal forces overcome self-gravity; closer than this, a moon is torn apart.
Rocket equation
Δv = u · ln(m₀ / m_f) — the velocity a rocket gains by expelling propellant, derived from momentum conservation.