Electric flow

Surname

Electric flow

${\ displaystyle {\ mathit {\ Psi}}}$

Size and unit system	unit	dimension
SI	C = A · s	I · T
Gauss ( cgs )	Fr.	M ^1/2 · L ^3/2 · T ⁻¹
esE ( cgs )	Fr.	M ^1/2 · L ^3/2 · T ⁻¹
emE ( cgs )	abC = Bi · s	L ^1/2 x M ^1/2

The electrical flow or displacement flow (Psi) is a physical quantity from electrostatics and electrodynamics . ${\ displaystyle {\ mathit {\ Psi}}}$

Although the electrical flow has mathematical properties that are similar to those of a real flow in a flow field , it does not transport anything material such as charge carriers , but only transfers the effect of the underlying force field from one point to another.

Depending on the context, the electrical flow is defined differently.

Electrotechnical definition

The following definition is usually used in electrical engineering literature. The relationships to matter and the relationship between fluxes and field strengths are described using the material equations of electrodynamics .

Since the electrical flow cannot be assigned to individual points in space (sometimes it is helpful to represent the flow with spatially extended flow tubes ), an electrical flow density is assigned to each point in space . Only that portion of the electrical flow contributes to the electrical flow through the surface that is normal to this surface. Mathematically, this fact is expressed in vector analysis by means of vectors and by the operation of the inner product as an area integral : ${\ displaystyle D}$ ${\ displaystyle A}$

{\ displaystyle {\ mathit {\ Psi}} = \ int \ limits _ {\ mathcal {A}} {\ vec {D}} \ cdot \ mathrm {d} {\ vec {A}}}

This results in the SI unit for this definition, ampere · second.

In the electrostatic case, the electrical flow can be visualized for the sake of simplicity:

the direction of the electric field strength at every point in space is represented by field lines which, by definition, point away from positive charges and towards negative charges.
The density of the electrical charges on the surfaces of the electrodes is represented by the density of the field lines on the conductor surfaces .
then the electrical flow that originates at an electrode or ends at it corresponds to the number of field lines that emanate from this electrode or end at it, and thus the amount of charge of this electrode.

This fact can also be expressed in such a way that an electrical voltage on a capacitor with the capacity transports a certain charge to the plates (electrodes) of the capacitor. This voltage causes an electrical flow of the size between the capacitor plates ${\ displaystyle U}$ ${\ displaystyle C}$

{\ displaystyle {\ mathit {\ Psi}} = C \ cdot U}

,

with which the electrical charge of the capacitor corresponds exactly to the electrical flow between the electrodes: ${\ displaystyle Q}$

{\ displaystyle {\ mathit {\ Psi}} = Q}

Physical definition

In the physical literature, for example in Gerthsen Physik , the electrical flow in a vacuum is specified in the form: ${\ displaystyle \ phi}$

{\ displaystyle \ phi = {\ frac {\ mathit {\ Psi}} {\ varepsilon _ {0}}} = \ int \ limits _ {\ mathcal {A}} {\ vec {E}} \ cdot \ mathrm {d} {\ vec {A}}}

with the electric field constant . ${\ displaystyle \ varepsilon _ {0}}$

This results in the SI unit volt meter for this definition .

Despite having the same name, this definition of electrical flow differs from the definition of electrical flow in electrical engineering; the electric flux here does not correspond to the area integral of the electric flux density , but to that of the electric field strength . In addition, this definition in matter, especially in the case of non-linear and anisotropic materials, results in complicated relationships. ${\ displaystyle \ phi}$ ${\ displaystyle {\ mathit {\ Psi}}}$ ${\ displaystyle \ phi}$ ${\ displaystyle D}$ ${\ displaystyle E}$

literature

Karl Küpfmüller, Gerhard Kohn: Theoretical electrical engineering and electronics . Springer, 1993, ISBN 3-540-56500-0 , pp. 80-88 .
Adolf J. Schwab: Conceptual world of field theory . Springer, 2002, ISBN 3-540-42018-5 , pp. 5-9 .
Dieter Metz, Uwe Naundorf, Jürgen Schlabbach: Small collection of formulas for electrical engineering . Carl Hanser, ISBN 3-446-22545-5 ( hanser.de [PDF]).

Individual evidence

↑ Dieter Meschede: Gerthsen Physik , 24th edition, Springer, 2010, ISBN 978-3-642-12893-6 , p. 318

[1] Dieter Meschede: Gerthsen Physik , 24th edition, Springer, 2010, ISBN 978-3-642-12893-6 , p. 318