THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Faraday's law
EMF = −dΦ_B/dt. The induced electromotive force in a closed loop equals the negative rate of change of magnetic flux through the loop. The first of Maxwell's time-dependent equations.
Fermat's principle
Light travels between two points along the path that takes the least time.
Ferroelectricity
The presence of a spontaneous electric polarization in certain crystals that can be reversed by an applied field — the electric analogue of ferromagnetism.
Ferromagnet
A material that holds a magnetisation with no external field, up to a sharp critical temperature at which it loses it.
Ferromagnetism
The spontaneous parallel alignment of atomic magnetic moments via quantum exchange interaction, producing permanent magnetization below a critical Curie temperature. The origin of magnetism in iron, nickel, cobalt, and everyday magnets.
Field energy density
The energy stored per unit volume in an electric field: u = ½ε₀E². Measured in joules per cubic metre.
Field line
A curve whose tangent at every point is the direction of the electric field there. Lines begin on positive charges and end on negative ones.
Field momentum
g = ε₀ E×B = S/c². The momentum density carried by the electromagnetic field. Integrated over a volume, it gives the total mechanical momentum the field carries, separate from the momentum of charges and currents.
First law of thermodynamics
Energy conservation for systems that exchange heat and work: ΔU = Q − W. Energy is never created or destroyed, only transferred or stored.
FLRW Metric
The unique spacetime line element for a universe that is the same everywhere and in every direction.
Fluctuation
The spontaneous deviation of a quantity from its mean in a system at thermal equilibrium.
Fluctuation–dissipation theorem
A system's spontaneous fluctuations and its dissipative response to a force are rigidly proportional, with k_BT the constant.
Flux
A scalar measure of how much of a vector field passes through a surface, weighted by the field's component normal to the surface.
Flux linkage
The total flux threading a multi-turn coil, summed across all turns: λ = N Φ for N turns each enclosing flux Φ. The quantity Faraday's law naturally refers to for real coils rather than single loops.
Focal length
f, the distance from a lens or mirror at which parallel incoming rays converge (or appear to diverge from). Positive for converging optics, negative for diverging. Determines magnification, angle of view, and depth of field.
focus
One of two interior points that define an ellipse; the central body sits at one focus in a Keplerian orbit.
force
A push or a pull; mathematically, the cause of acceleration — F = ma.
Forced oscillation
An oscillator being driven by a periodic external force, settling into a steady state at the drive frequency.
Four-acceleration
The Lorentz four-vector a^μ = du^μ/dτ, the second proper-time derivative of a particle's spacetime trajectory. Always orthogonal to four-velocity in the Minkowski metric (a^μ u_μ = 0); non-zero only on accelerated (non-geodesic) world-lines; reduces to the ordinary three-acceleration in the instantaneous rest frame.
Four-current
The Lorentz four-vector J^μ = (cρ, J_x, J_y, J_z) packaging charge density and current density into a single covariant object. Sources the field tensor F^{μν} via Maxwell's equation ∂_μ F^{μν} = μ₀ J^ν.
Four-force
The Lorentz four-vector F^μ = dp^μ/dτ; the relativistic generalisation of Newton's force. For a particle of constant rest mass, F^μ = m·a^μ. The time component is the rate of energy transfer (power); the spatial components reduce to Newton's second law in the low-β limit.
Four-momentum
The Lorentz four-vector p^μ = (E/c, p_x, p_y, p_z) combining a particle's energy and three-momentum into a single object that transforms covariantly under boosts. Its invariant norm-squared p^μ p_μ = (E/c)² − |p|² = m²c² is the energy-momentum-mass relation; total four-momentum is conserved in any collision.
Four-potential
The Lorentz four-vector A^μ = (φ/c, A_x, A_y, A_z) packaging the scalar potential φ and vector potential A into one covariant object. The fundamental dynamical variable of electromagnetism in the Lagrangian formulation; the EM field tensor F^{μν} = ∂^μA^ν − ∂^νA^μ.
Four-vector
A quantity X^μ = (X⁰, X¹, X², X³) that transforms under Lorentz boosts the same way the spacetime coordinates (ct, x, y, z) do. The natural container for any pair of scalar-plus-three-vector quantities in special relativity.
Four-velocity
The Lorentz four-vector u^μ = dx^μ/dτ = γ(c, v_x, v_y, v_z), the tangent to a particle's timelike world-line parametrized by proper time. Its norm u^μ u_μ = c² is constant on every timelike world-line; differentiating it gives four-acceleration, and m·u^μ is the four-momentum.
Fourier series
The decomposition of an arbitrary periodic function into a sum of sines and cosines.
Frame Dragging
A rotating mass twists the spacetime around it, forcing nearby objects to co-rotate.
Free expansion
A gas rushing into a vacuum: no work done, no heat exchanged, so ΔU = 0 — and for an ideal gas, no change in temperature.
free fall
Motion under gravity alone, with no air resistance or other forces — every object accelerates at the same rate.
Frequency
Number of oscillation cycles per unit time, symbol f, measured in hertz.