Electric current density
|Surname||Electric current density|
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Furthermore, in non-homogeneous flow fields, the current density can be used to indicate how the current is distributed point by point over the cross-sectional area. Such applications relate, for example, to gas discharges and electron beams as well as the loading of electrodes and hot cathodes .
In classical physics:
The vector is perpendicular to the associated surface element. If the current density is evenly distributed over the cross-sectional area (e.g. if direct current flows through a metallic conductor), the definition is simplified to . The scalar product is reduced under simple model calculations for vertically-carrying surface (in the picture) to the elementary product : .
- a considered volume,
- the total electrical charge in this volume,
- the charge carrier density (number of charge carriers per volume),
- the charge of a single charge carrier ( elementary charge ; 1.60 · 10 −19 As),
- the space charge density ,
- the location coordinate in the direction of flow,
- the time,
- the mean drift speed of the charge carriers,
- the current strength (charge per time)
results from an arrangement as in the figure with a current flowing evenly over the cross-sectional area and flowing in the x-direction (perpendicular to the marked yz-plane)
The current density is a vector quantity whose direction corresponds to that of the velocity vector of positive charge carriers:
With regard to the electrical current, the current strength is preferably used in practical electrical engineering for bills ,
- for example, one chooses the notation for Ohm's law
In contrast, in theoretical electrical engineering, the current density is usually used,
- for example, one chooses the notation for Ohm's law
Current density in lines
The density of the conductor current in copper windings may not exceed 1.2 ... 6 A / mm 2 , depending on the application , so that no inadmissible heating occurs under continuous load . This is also referred to as current carrying capacity . In extreme cases, however, it can rise to a melt current density of 3060 A / mm 2 . The heating in fuses is used to interrupt the current. In conductors, the maximum current strength according to VDE 0298-4: 2013-06, table 11 and column 5 is:
- 12 A with a cross-sectional area of 0.75 mm 2 ,
- 15 A at 1.0 mm 2 and
- 26 A at 2.5 mm 2 .
With a current density evenly distributed over the cross-section, the average speed in the conductor is the same . The typical electron density for conduction electrons in metallic solids is in the order of magnitude of = 10 28 m −3 . If one takes into account that in a positive half-oscillation of an alternating current, the mean current intensity is smaller than its effective value by the factor ( = form factor , with sine curve = 1.11), then with a current density of 6 A / mm 2 for a directional movement a mean speed of the order of 10 −3 m / s. The high speed of electrical communication is not based on the displacement of the electrons in the wire.
In the case of alternating current , the skin effect must be observed, according to which the current density inside a conductor is lower than on the surface. For orientation, the depth is given for a decrease in the current density to 1 / e = 37%. In thick, solid aluminum or copper round conductors, it is around 10 mm at 50 Hz.
In electroplating , the current density that is set for the coating is specified. The typical values are between 0.5 and 5 A / dm 2 , which must be observed in order to e.g. B. to get good results with a galvanizing or nickel plating .
In the case of solar cells , one rather specifies a power density. It can be very roughly up to 150 W / m 2 . The electrical voltage at maximum power in the most common cells is around 0.5 V, so that a current density of up to 300 A / m 2 can result.
Correspondingly, fuel cells are also examined depending on their current densities, in particularly favorable cases up to about 1 A / cm 2 .
Surface current density and line current
Analogous to the current density in a body, the current density can also be related to two-dimensional surfaces. This assumption is useful if you want to describe the surface conduction ( leakage current ) of electrical insulators . The total flow is the sum of the individual area flows. The surface current density is obtained by relating the total current to the width of the individual surface:
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- DIN 1304-1: 1994 Formula symbols - General formula symbols .
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- Melting current density is the current density at which the conductor temperature rises to melting temperature after 1/100 s load. Value according to Müller-Hildebrand
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