Abstract:
The calculation of the magnetic field of currents has important practical and methodological
significance. The determination of the magnetic field of current in massive conductors is based
on the integration over the entire volume of the conductor of the magnetic fields created by the
current elements. It is much easier to calculate the field using the linear current model, but the
conditions of its application (the parameters of the conductor cross-section must be much smaller
than the distance to the observation point) are idealized and limit the practical application of
the model. The literature considers the magnetic field of currents in cylindrical conductors, but
in practice, conductors with a rectangular cross-section are used. The purpose of the work is to
obtain mathematical expressions for determining the induction of the magnetic field generated
by a direct current in a straight long conductor with a rectangular cross-section, on the axes of
symmetry of the cross-section, and to calculate the error of applying the linear current model
for this, depending on the relative distance to the observation points. For points on the Ox axis
(in the direction of the cross-section width), the values of the true magnetic field induction B
are greater than the linear current field, and for points on the Ou axis, on the contrary, they are
smaller. With an increase in the degree of elongation of the conductor cross-section (decreasing
c), the absolute and relative errors of the application of the linear current model increase, since
in this case the conductor and its field increasingly differ from a cylindrical conductor, the field
of which, like the linear current field, is cylindrically symmetrical. The results of the work have
significant practical significance and can be used in the development of electrical devices to
determine the true magnetic field, or approximately in the linear current model with a known
error. The methodological significance of the work lies in demonstrating the limitations of the
application of models in physics and the dependence of the model error on the conditions of its
application.
