# Flux

Flux is a mathematical concept that describes the "flow" of a vector field through an area. It comes from the Latin, fluxus, meaning "flow".[1] It is a scalar quantity, usually denoted using the Greek letter ϕ and defined mathematically as:



for a vector field F. The flux depends on the density of the field lines in the vector field, the orientation of the area to the vector field and the size of the area. As an example, consider water flowing along a river. The vector field would be the velocity of the water at each point in the river. The flux across an area in the river would be equal to the rate of flow of water through that area.

## Example

Flux is a very important concept in physics, particularly electromagnetism. Faraday's Law of electromagnetic induction relates the voltage produced by moving a coil of wire to the rate of change of magnetic flux. If a loop with an area A is placed in a magnetic field, B, the flux through the loop is:



If the magnetic field is uniform and at an angle θ, to the normal of the loop, then the flux can be written as:



Note that the flux is zero when θ=90 and maximum when θ=0.