flux

Flux is a term used in physics, engineering, and mathematics to describe the rate at which a quantity passes through a surface or boundary, typically per unit area. In mathematical terms, the flux of a vector field F through a surface S is the surface integral ∫∫_S F · n dS, where n is the chosen unit normal to S. The concept depends on the surface orientation and on the field being measured.

Common types of flux include:

- Magnetic flux, Φ_B = ∫∫_S B · dA, with the Weber as the SI unit. Magnetic flux links to Faraday's law and electromagnetic induction.

- Electric flux, Φ_E = ∫∫_S E · dA; Gauss's law relates the flux through a closed surface to the enclosed charge.

- Heat or thermal flux, often written q'' for heat transfer per unit area; Fourier's law states q'' = -k ∇T.

- Volumetric or mass flux in fluids, Q = ∫∫_S v · dA, representing the rate of fluid passage through S; related to continuity and energy equations.

- Diffusive or particle flux, J = -D ∇c, as in Fick's law for concentration gradients.

- Radiant or luminous flux, Φ for radiant power; luminance contexts use lumen as the photometric unit.

Other uses: in metallurgy and electronics, flux is a chemical cleaning agent that removes oxides and facilitates bonding during soldering and brazing.

In summary, flux quantifies how much of a quantity crosses a boundary per unit area, forming a bridge between local field values and total transfer across surfaces.