ERROR IN THE APPLICATION OF COULON'S LAW TO THE INTERACTION OF CHARGED RODS

Abstract

Formulation of the problem. Determining the force of interaction of charged bodies is of significant practical and methodical importance. It is based on Coulomb's law, but it defines the interaction between point charges. The idealized condition for the implementation of the law (the sizes of the bodies are much smaller distances between them) does not allow using it to solve practical problems. In the case of a small distance between charged bodies, the model of a continuously distributed charge is used, and the interaction force is calculated by integrating the interaction forces of the elements of the bodies over the volume of the bodies, which complicates the practical use of this model.

Materials and methods. The results of calculating the force of interaction between two uniformly charged rods according to different models were compared. The true force was determined in the continuously distributed charge model, the Coulomb force in the point model. The absolute and relative errors of the application of Coulomb's law were calculated depending on the relative distance , where a is the distance between the centers of charges, L is the length of the rods.

Results. The scientific novelty of the work consists in determining the error of applying Coulomb's law to the calculation of the force of interaction between charged rods depending on the relative distance between them. It decreases with increasing relative distance and depends on the mutual orientation of the rods. The error has the greatest value when the rods are located on one axis.

Conclusions. Calculations showed that Coulomb's law can be applied to determine the force of interaction between charged bodies even at small values of the relative distance between them. For different mutual orientation of the rods, the relative distance at which the error of applying Coulomb's law becomes less than 0.5% should be greater than 5 to 8 units. Since rods are a vivid representative of elongated bodies, for which the condition of applying the point charge model is unfavorable, the obtained results can be used in determining the interaction of bodies of arbitrary shape.