# Electricity (physics)

In physics, a stream is the transport of a quantity-like quantity . Its measures are the current strength and the current density .

A stream is a special flow that is characterized by the fact that a quantifiable amount is transported. A similar analogy applies to current density and flux density . The specialization in electricity and flow is not common in all languages, for example “heat flux” denotes the heat flow in English . In quantum physics , electricity also means the transport of a quantity-like quantity between states - quasi through their interface in the state space (for example, charged and neutral currents in the weak interaction ).

If the quantity-like quantity is a conserved quantity , then a flow is the only possibility to change the quantity of this quantity in a volume element (because no sources and sinks can exist that would cause other changes).

## Amperage

The word "current" often means the strength of the current . It is defined as the magnitude of the quantity that moves through a (surface) area per time interval : ${\ displaystyle I}$${\ displaystyle Q}$${\ displaystyle t}$

${\ displaystyle I = {\ frac {\ partial Q} {\ partial t}} \ Leftrightarrow Q = \ int _ {t} I \ cdot \ mathrm {d} t}$

The current strength is a directed quantity which always applies to a single volume and its edge, i.e. H. its surface, is related. The surface of the volume is understood as an oriented surface . The current intensity is the measure of the flow of this volume also , so that shows signs of its size value , the current direction of.

## Current density

The current density is a vector quantity . Its magnitude , also called intensity , is the amount that leaves the volume per time interval and (upper) area , and its direction is that of the mean drift speed of the movement: ${\ displaystyle {\ vec {j}}}$ ${\ displaystyle j}$${\ displaystyle \ partial A}$

${\ displaystyle {\ vec {j}} = {\ frac {\ partial I} {\ partial {\ vec {A}}}} = {\ frac {\ partial ^ {2} Q} {\ partial t \ cdot \ partial {\ vec {A}}}}}$

Conversely, the current strength results mathematically as the area integral over the current density, clearly by adding up all current densities perpendicular to the surface:

${\ displaystyle I (\ partial {\ mathcal {V}}) = \ int _ {\ partial {\ mathcal {V}}} {\ vec {j}} \ cdot \ mathrm {d} {\ vec {A} }}$,

where denotes the entire edge of the volume , i.e. the surface of the volume. ${\ displaystyle \ partial {\ mathcal {V}}}$${\ displaystyle {\ mathcal {V}}}$

## Mathematical formulation

The (extended) continuity equation applies :

${\ displaystyle \ partial _ {t} \ rho = f - {\ vec {\ nabla}} \ cdot {\ vec {j}}}$

With

• the density of the quantity in a volume${\ displaystyle \ rho}$${\ displaystyle Q}$${\ displaystyle {\ mathcal {V}}}$
• the density of the rate of generation of the quantity-like quantity in the volume${\ displaystyle f}$${\ displaystyle F}$${\ displaystyle {\ mathcal {V}}}$
• the derivative of time ${\ displaystyle \ partial _ {t}}$
• the divergence operator .${\ displaystyle {\ vec {\ nabla}} \ cdot}$

Based on the Gaussian integral theorem then applies

${\ displaystyle \ partial _ {t} Q ({\ mathcal {V}}) = F ({\ mathcal {V}}) - I (\ partial {\ mathcal {V}})}$.

The quantity-like size and its density are connected via the volume integral :

${\ displaystyle Q ({\ mathcal {V}}) = \ int _ {\ mathcal {V}} \ mathrm {\ rho} \, dV}$.

## application

For example, currents are considered in mechanics, thermodynamics, acoustics, optics, electricity, neutron physics and particle physics. The terms mass flow and volume flow are common for the movement of matter . For incompressible fluids like water, the volume can be viewed as a quantity.

If the quantitative quantities of thermal energy or electrical charge are carried along by moving matter, one speaks of convection current .

The Karlsruhe physics course strongly expands on such analogies and also advocates the idea of ​​an entropy and momentum stream in order to avoid Newton's idea of force and counterforce .

## literature

• Hans Moor: Physical principles of construction and energy , vdf, Zurich 1993, vol. 1, p. 12f. ISBN 9783728118240
• Norbert Pucker: Physical basics of energy technology , Springer, Vienna 1986, p. 20f. ISBN 978-3-211-81948-7

## Individual evidence

1. Heiner Schwarze et al. (Ed.): Everything flows , volume 1 in: Praxis der Wissenschaft im Schule , 61: 2012.