Density of current

The density of current electric is defined like the Electric current per unit of area (figure). Mathematically, the current and the density of current are bound by the relation:

$I= \ int_Sj (there, Z) .dS \,$

* I is the Electric current in amps has

* J (there, Z) is the density of current at the point of coordinates (there, Z) in A.m^-2

* S is the section in m²

If the density of current is homogeneous, i.e. if J (there, Z) is a constant independent of the position (there, Z), then the relation is simplified and becomes:

$I=j.S \,$

The density of current is related to the charge carriers (electron S, holes, Ion S in a electrolyte) by the relation:

$j= \ sum_in_i.x_i.v_i \,$

* n_i is the Concentration carrier I (the number of carriers per unit of volume)

* x_i is the load carrier I

* v_i is the mean velocity of carrier I in

volume

The density of current in a material is a very important parameter in the electric or electronic systems. It is indeed directly related to the Chaleur produced in material by Joule effect. Each element of volume of material will produce Chaleur according to:

$p=j^2_ {EFF}. \ rho \,$

* p is the thermal power produced per unit of volume (in W/m³)

* j_eff is the effective value of J (T), which must be, at any moment, identical in any point of volume considered

* ρ is resistivity of the material

For the ordinary drivers, the density of current must thus be kept sufficiently low in each point of material to prevent that the Isolant external of the driver is not destroyed under the effect of the Chaleur produced by Joule effect. According to the type of employment, the density of current not to be exceeded varies between 3 and 5 A/mm². With contrario, one chooses in certain devices, either of the sufficiently large densities of current to cause the fusion of the driver (principle of the furnaces with induction with channel), or of materials able to melt starting from a density of current given (principle of the Fusible S).

In the materials superconductive S, a too high density of current can generate a sufficient Magnetic field to cause the loss of the superconductive state .

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