Current density

The electric current density (symbol ( as in ), or also ) indicates how crowded together, an electric current flows. This characterizes the burden of a conductor by the current.

The current density is defined as the ratio of the current to the current to the available cross -sectional area through which the current passes perpendicular.

Next can be specified in a non- homogeneous flow fields with the current density as the current point-wise distributed over the cross-sectional area. Such applications include gas discharges and electron beams as well as the burden of electrodes and hot cathodes.

Definition

In classical physics, the following applies:

The vector is perpendicular to the corresponding surface element. The current density is evenly distributed across the cross-sectional area ( for example, when direct current flows through a metal conductor ), then the definition reduces to. The scalar product is reduced in the framework of simple model calculations with vertically -carrying surface (as in the picture) to the vital product.

With

Resulting in an arrangement as in the image with uniformly distributed over the cross-sectional area, in the x direction (perpendicular to the marked plane yz ) current flowing

The current density is a vector quantity whose direction coincides with that of the velocity vector of the charge carriers.

For the definition of the current density in quantum field theory, see probability current density.

Applications

Calculations

With respect to the electric current, the current is in the practical case of invoices electrical preferably used

In contrast, the current density is in the theoretical electrical commonly used

With the electrical conductivity, the electrical voltage,

Thus, the vector current density is used for example in the Maxwell equations and the continuity equation of electrodynamics.

Current density in lines

The density of the conductor current in copper windings may vary depending on application 1.2 ... 6 A/mm2 not exceed, thus under constant load without excessive heating occurs. However, in extreme cases, it can rise up to the melting current density of 3060 A/mm2. In fuses heating is used to interrupt the current. In conductors the maximum allowable current to VDE 0298-4:2013-06, Table 11 and column 5 of 12 A at a cross-sectional area of 0.75 mm2, 15 A at 1.0 mm2 and 26 A with 2.5 mm2.

At a current density uniformly distributed over the cross section, the average speed in the conductor is the same. The typical electron density for conduction electrons in the metallic solids on the order of 1028 m = 3rd Taking into account that in a positive half cycle of an alternating current, the average current over its effective value is smaller by a factor ( = form factor for sinusoidal curve = 1.11 ), we obtain at a current density of 6 A/mm2 a medium for a directed movement speed on the order of 10-3 m / s The high speed of the electric communication is not based on the movement of the electrons in the wire.

Wherein alternating current skin effect is observed, after which the current density inside of a conductor is lower than at the surface. For guidance adding the depth to a decrease in the current density to 1 / e = 37%. In thick solid aluminum or copper circular conductors it is at 50 Hz around 10 mm.

Electroplating

In electroplating, the current density is one that is set for the coating of. Typical values ​​are between 0.5 and 5 dm 2, which must be adhered to, for example, to obtain good results in a zinc or nickel plating.

Power sources

In solar cells, you are more of a power density. It can be very rough to 150 W/m2. The electric voltage at maximum power is the most commonly used cells at about 0.5 V, so that a current density may result in up to 300 A/m2.

Accordingly, one can also examined as a function of their fuel cell power densities, in a particularly favorable cases up to about 1 A/cm2.

Surface current density and line current

Analogously to the current density in a body can also refer to the current density, two-dimensional surfaces. This assumption is useful if you want to describe about the surface conduction ( leakage ) of electrical insulators. The total current is the sum of the surface currents. The surface current density is obtained by referring the entire current to the width of each surface:

The electrical current can also be also considered as a sum of line currents in a point, from which the first Kirchhoff's rule follows: