Current density in a wire shows as far as this wire electrically is loaded. To avoid excessive losses or rise in price of conducting, current density in it is taken optimum – economic. For high frequencies (radio, TV) at the same time should consider additional electrodynamic effects.
Density of direct electric current can be compared to density of the gas flowing in a pipe under pressure. Density of current is equal to the current relation in amperes (A) to the cross-sectional area of the conductor in square millimeters (Poses. 1 in the drawing). Its value does not depend on material of the conductor. Section of the conductor undertakes on a normal (perpendicularly) to its longitudinal axis.
If, let us assume, the wire has diameter of D = 1 mm, then the area of its cross section will be S = 1/4 (πD^2) = 3.1415/4 = 0.785 sq. mm. If on such wire the current of I in 5 A flows, then its density to j will be equal to j = to I/S = 5/0.785 = 6.37 A/sq. mm.
Values of density of current in the equipment
Though the value of density of current does not depend on material of the conductor, in the equipment it is chosen, proceeding from its specific electrical resistance and length of a wire. The fact is that at the big density of current the conductor with it heats up, its resistance from it increases, and losses of the electric power in conducting or a winding increase. However, if to take wires too thick, then and all conducting will turn out excessively expensive. Therefore calculation of household conducting is conducted, proceeding from the so-called economic density of current at which the total long-term costs of the power supply network are minimum. For room conducting in which wires not really long, take value of economic density within 6-15 A/sq. mm. depending on length of wires. The copper wire with a diameter of 1.78 mm (2.5 sq. mm) in the isolation PVC immured under plaster will sustain both 30, and even 50 amperes. But at the power consumed by the apartment in 5 kW density current in it will be (5000/220) = 23 A, and its density in conducting – 9.2 A/sq. mm. The economic density of current in power lines is much lower, within 1-3.4 A/sq. mm. In electrical machines and transformers of the industrial frequency of 50/60 Hz – from 1 to 10 And / sq. mm. In the latter case it is calculated, proceeding from admissible heating of windings and size of electric losses.
About density of current of high frequency
Density of current of high frequencies (a body and radio signals, for example) is counted taking into account a so-called skin-effect (skin is in English "skin"). Its essence that the electromagnetic field pushes aside current to a wire surface therefore for obtaining its necessary density it is necessary to take diameter of a wire more and not to spend excess copper, to do it hollow, in the form of a tube. The skin-effect matters not only by transfer of big capacities. If, let us assume, to make distributing of cable television on the apartment too thin coaxial cable, then losses in it because of a skin-effect in an internal wire can be excessively big. Analog channels will flicker at the same time, and digital – to be scattered in small squares. Depth of a skin-effect depends on signal frequency, and current density at the same time smoothly reduces to zero in the center of a wire. In the equipment for simplification of calculations the depth a skin surface is considered where density of current falls by 2.72 times in comparison with superficial (Poses. 2 in the drawing). Size 2.72 is brought in technical electrodynamics out of a ratio of an electric and magnetic constant that facilitates calculations.
Shift current density
Shift current quite difficult concept of electrodynamics, but exactly thanks to it passes alternating current through the condenser, and the antenna radiates a signal in air. Shift current has the density too, but it is not so simple to determine it. Even in very good condenser the electric field slightly "sticks out" in the parties between plates (Poses. 3 in the drawing) therefore to the surface crossed by current of shift it is necessary to give some additive. For the condenser its size still can be neglected, but if the speech about the antenna, then there this the virtual, crossed by shift current surface means all. To find shift current density, it is necessary to solve the difficult equations of electrodynamics or to make computer modeling of process. Fortunately, for many cases of engineering practice the nobility her size is not required.