EQUATION OF LINES OF FORCE OF THE ELECTROSTATIC FIELD IN CERTAIN CASES - Avdonin, Kostiantyn; Zubko, Oleksandr (Physical and Mathematical Education, 2024)
In this work, the equations of the lines of force of the electrostatic field are searched in an explicit form, which is possible, of course, only in certain cases. The relevance of the work is due to the need to supplement the methodology of presenting such an important topic of the general physics course as «Electrostatics» in the field of means of graphic representation of the electrostatic field, which contributes to a better understanding of this topic. Cases were found and considered for which the equations of force lines exist in an explicit form. For each individual case, an example of the appearance of the lines of force of the electrostatic field, which follows from the obtained equations, is given using the package of applied computing programs MathCAD. The construction of power lines of the electrostatic field, of course, can be carried out using only numerical methods, based on the definition of the tangent to the line. Still, this approach significantly increases the complexity of computing programs. Formulation of the problem. The lines of force of the electrostatic field in textbooks and teaching aids for the course of general physics draw, based on the definition of lines of force and formulas, expressions for the intensity of the electrostatic field, without obtaining the equations of the lines of force of the field, that is, it is insufficiently substantiated. Materials and methods. The main methods of solving the problem are finding solutions to a system of ordinary, nonlinear, differential equations and using graphical operators in the environment of MathCAD applied computing programs. Results. It was found that the equations of force lines exist in an explicit form for the electric field of two-point charges and for the electric field of a rectilinear, uniformly charged thread of finite length. Examples of lines of force are given, the general appearance of which is consistent with the known boundary conditions. Conclusions. The obtained equations of the lines of force of the electrostatic field make it possible to strengthen the completeness of the presentation of the material in the "Electrostatics" section. Graphs of field lines of force, built with the help of computer programs, increase the level of proof of the presentation of the material and contribute to its understanding.