Flux is either of two separate simple and ubiquitous concepts throughout physics and applied mathematics. source
Flux is either of two separate simple and ubiquitous concepts throughout physics and applied mathematics.
Flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. source
Flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property.
In electromagnetism, flux is a scalar quantity, defined as the surface integral of the component of a vector field perpendicular to the surface at each point. source
In electromagnetism, flux is a scalar quantity, defined as the surface integral of the component of a vector field perpendicular to the surface at each point.
The word flux comes from Latin: fluxus means "flow", and fluere is "to flow". source
The word flux comes from Latin: fluxus means "flow", and fluere is "to flow".
In the case of fluxes, we have to take the integral, over a surface, of the flux through every element of the surface. source
In the case of fluxes, we have to take the integral, over a surface, of the flux through every element of the surface.
The result of this operation is called the surface integral of the flux. It represents the quantity which passes through the surface. source
The result of this operation is called the surface integral of the flux. It represents the quantity which passes through the surface.
According to the first definition, flux may be a single vector, or flux may be a vector field / function of position. source
According to the first definition, flux may be a single vector, or flux may be a vector field / function of position.
In the latter case flux can readily be integrated over a surface. source
In the latter case flux can readily be integrated over a surface.
By contrast, according to the second definition, flux is the integral over a surface. source
By contrast, according to the second definition, flux is the integral over a surface.
Thus, Maxwell's quote only makes sense if "flux" is being used according to the first definition (and furthermore is a vector field rather than single vector). source
Thus, Maxwell's quote only makes sense if "flux" is being used according to the first definition (and furthermore is a vector field rather than single vector).
This implies that Maxwell conceived as these fields as flows/fluxes of some sort. source
This implies that Maxwell conceived as these fields as flows/fluxes of some sort.
it makes no sense to integrate a second-definition flux for one would be integrating over a surface twice. source
it makes no sense to integrate a second-definition flux for one would be integrating over a surface twice.
Given a flux according to the second definition, the corresponding flux density. source
Given a flux according to the second definition, the corresponding flux density.
By the Fundamental theorem of calculus, the corresponding flux density is a flux according to the first definition. source
By the Fundamental theorem of calculus, the corresponding flux density is a flux according to the first definition.
Given a current such as electric current—charge per time, current density would also be a flux according to the first definition . source
Given a current such as electric current—charge per time, current density would also be a flux according to the first definition .
Due to the conflicting definitions of flux, and the interchangeability of flux, flow, and current in nontechnical English, source
Due to the conflicting definitions of flux, and the interchangeability of flux, flow, and current in nontechnical English,
Concrete fluxes in the rest of this article will be used in accordance to their broad acceptance in the literature, source
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. source
Regardless of which definition of flux the term corresponds to.
For vector flux, the surface integral of j over a surface S, gives the proper flowing per unit of time through the surface. source
For vector flux, the surface integral of j over a surface S, gives the proper flowing per unit of time through the surface.
Momentum flux, the rate of transfer of momentum across a unit area (N·s·m−2·s−1). (Newton's law of viscosity). source
Momentum flux, the rate of transfer of momentum across a unit area (N·s·m−2·s−1). (Newton's law of viscosity).
Heat flux, the rate of heat flow across a unit area (J·m−2·s−1). (Fourier's law of conduction) (This definition of heat flux fits Maxwell's original definition.) source
Heat flux, the rate of heat flow across a unit area (J·m−2·s−1). (Fourier's law of conduction) (This definition of heat flux fits Maxwell's original definition.)
This flux has units of mol·m−2·s−1, and fits Maxwell's original definition of flux. source
This flux has units of mol·m−2·s−1, and fits Maxwell's original definition of flux.
One way to better understand the concept of flux in electromagnetism is by comparing it to a butterfly net. source
One way to better understand the concept of flux in electromagnetism is by comparing it to a butterfly net.
The flux of the Poynting vector S over a specified surface is the rate at which electromagnetic energy flows through that surface. source
The flux of the Poynting vector S over a specified surface is the rate at which electromagnetic energy flows through that surface.
