Аннотации:
The calculation of the electric field of charged bodies is performed on
the basis of point and continuously distributed charge models. The true field near
the bodies is calculated using the second model, but this process requires high
qualification and complex mathematical calculations. It is much easier to
determine the field using the point charge model, but the condition of its
application (the distance to the observation point is much larger than the size of
the body) is idealized and limits its practical application. Mathematical
expressions for the dependence of the true electrostatic field strength of a square
uniformly charged plate on the relative distance to the observation point in the
directions of the symmetry axes of the plate have been obtained. Their reliability is
confirmed by the fact that at a large distance, when b/l→∞, the field strength is
zero. The error of applying the point charge model to determine the electrostatic
field of a square plate depending on the relative distance to the observation point
in the directions of the symmetry axes of the plate, where it has extreme values, has
been calculated. The results of the calculations show that when approaching the
body, the error increases sharply and tends to zero at a large distance. The error
is less than 0.5% when the relative distance becomes larger: 5 - in the direction of
the axis of symmetry perpendicular to the side of the plate, 8 - in the direction of
the axis perpendicular to the plane of the plate. The mathematical expressions for
determining the electrostatic field strength of a square plate and the error of
applying the point charge model depending on the relative distance to the
observation point were obtained independently, we are not aware of the literature
data, therefore the obtained results have scientific novelty. The results of the work
have significant practical significance and can be used in the development of
electrical devices to determine the true electric field, or approximated in the point
charge model with a known error. It is important that the point charge model can
be used in cases where the relative distance to the observation point is only a few
units, and not “much more”, as given in the methodological literature. The
methodological significance of the work lies in demonstrating the limitations of the
application of physical models and the dependence of the error on the conditions
of use of the model.
