ELECTRIC FIELD TENSION OF A SQUARE PLATE AND ERROR OF ITS DETERMINATION USING THE POINT CHARGE MODEL

Abstract

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.