Concrete fluxes in the rest of this article will be used in accordance to their broad acceptance in the literature, regardless of which definition of flux the term corresponds to. Due to the conflicting definitions of flux, and the interchangeability of flux, flow, and current in nontechnical English, all of the terms used in this paragraph are sometimes used interchangeably and ambiguously.
Given a current such as electric current-charge per time, current density would also be a flux according to the transport definition-charge per time per area. By the Fundamental theorem of calculus, the corresponding flux density is a flux according to the transport definition. Given a flux according to the electromagnetism definition, the corresponding flux density, if that term is used, refers to its derivative along the surface that was integrated. This implies that Maxwell conceived of these fields as flows/fluxes of some sort. Their names in accordance with the quote (and transport definition) would be "surface integral of electric flux" and "surface integral of magnetic flux", in which case "electric flux" would instead be defined as "electric field" and "magnetic flux" defined as "magnetic field". This is ironic because Maxwell was one of the major developers of what we now call "electric flux" and "magnetic flux" according to the electromagnetism definition. Thus, Maxwell's quote only makes sense if "flux" is being used according to the transport definition (and furthermore is a vector field rather than single vector). By contrast, according to the electromagnetism definition, flux is the integral over a surface it makes no sense to integrate a second-definition flux for one would be integrating over a surface twice. In the latter case flux can readily be integrated over a surface. It represents the quantity which passes through the surface.Īccording to the transport definition, flux may be a single vector, or it may be a vector field / function of position. The result of this operation is called the surface integral of the flux. In the case of fluxes, we have to take the integral, over a surface, of the flux through every element of the surface. One could argue, based on the work of James Clerk Maxwell, that the transport definition precedes the definition of flux used in electromagnetism.
His seminal treatise Théorie analytique de la chaleur ( The Analytical Theory of Heat), defines fluxion as a central quantity and proceeds to derive the now well-known expressions of flux in terms of temperature differences across a slab, and then more generally in terms of temperature gradients or differentials of temperature, across other geometries. The concept of heat flux was a key contribution of Joseph Fourier, in the analysis of heat transfer phenomena. As fluxion, this term was introduced into differential calculus by Isaac Newton. The word flux comes from Latin: fluxus means "flow", and fluere is "to flow". In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. Flux is a concept in applied mathematics and vector calculus which has many applications to physics.
#DEFINITION OF FYELS PATCH#
n, dS for each patch on the surface is the flux through the surfaceįlux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance.The flux through each patch is equal to the normal (perpendicular) component of the field, the dot product of F( x) with the unit normal vector n( x) (blue arrows) at the point x multiplied by the area dS. To calculate the flux of a vector field F (red arrows) through a surface S the surface is divided into small patches dS.
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