Source and sink

This article covers sources and sinks of physical fields. For sources and sinks of directed graphs see degrees (graph theory) .

Source and sink

In mathematics and physics, source and sink are terms from vector analysis , potential theory and field theory . They represent the starting and end points of currents or field lines . Both types of points can be distributed both singularly and continuously on lines, surfaces and spaces. Sources and sinks of a vector field are mathematically described by the source density ( divergence ): ${\displaystyle {\vec {F}}({\vec {r}})}$ ${\displaystyle q({\vec {r}})}$

${\displaystyle \mathrm {div} {\vec {F}}({\vec {r}})=q({\vec {r}}){\begin{cases}>0,&{\text{Quelle}}\\=0,&{\text{quellenfrei}}\\<0,&{\text{Senke}}\end{cases}}}$

The term source-free means that neither sources nor sinks exist.

Potential field

Many potential fields ( force fields such as the earth's gravitational field or electrostatic fields ) with their field lines extend infinitely far into the outer space . A sink is not defined for these static fields.

Electrical measurement technology

Every measurement loads a source or a field through a temporary or constant discharge of charge, matter or energy. The measuring instrument or the measuring arrangement thus forms a sink as the location of a measurement where the flow produces a physically measurable effect.

Examples

• A vivid example of a source and a sink is a sink with a tap (source) and drain (sink).
• A technical application example consists in the calculation of wing profiles in which a source / sink distribution (so-called "singularities") is superimposed on a simple flow field on the profile chord ( profile theory according to the singularity method ).
• Sources of gravitational fields are all mass points in the interior of celestial bodies
• Sources of an electric field are positive charges , sinks are negative charges.
• The magnetic field is "source-free", it has neither sources nor sinks.