Flux

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This article is about the concept of flux in science and mathematics. For other uses of the word, see Flux (disambiguation).

In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.

• In the study of transport phenomena (heat transfer, mass transfer and fluid dynamics), flux is defined as the amount that flows through a unit area per unit time^[1] Flux in this definition is a vector.
• In the field of electromagnetism and mathematics, flux is usually the integral of a vector quantity, flux density, over a finite surface. It is an integral operator that acts on a vector field similarly to the gradient, divergence and curl operators found in vector analysis. The result of this integration is a scalar quantity called flux.^[2] The magnetic flux is thus the integral of the magnetic vector field B over a surface, and the electric flux is defined similarly. Using this definition, the flux of the Poynting vector over a specified surface is the rate at which electromagnetic energy flows through that surface. Confusingly, the Poynting vector is sometimes called the power flux, which is an example of the first usage of flux, above.^[3] It has units of watts per square metre(W/m²)
  In this context, flux has a primary mathematical definition in terms of a surface integral which uses the vectors that represent the force which is causing the flux being studied: