The contribution to the deeper understanding of the field operators in electromagnetic field theory


The successful study of electromagnetic problems depends on a large extent from a good understanding of several field operators that are frequently used when describing these problems. It regards mainly the gradient, divergence, curling (or rotation) and Laplace's operators. Many years experience tell us that the good understanding of the mathematical and especially the physical meaning of these operators can encourage the students to study hard the demanding parts of electromagnetic field theory and opposite the insufficient coping with this topics block out them from further successful individual study. This is why we have tried to offer this aid to students when they meet this topic within their university study. The presentation offered consists of four parts. First and second parts are preparatory and deal with the definitions of curvilinear orthogonal coordinate system generally (first part) and the basic properties of the three most frequently used curvelinear orthogonal systems - cartesian, circular cylindrical and spherical ones (second part). The third part is devoted to the definitions of basic field operators in the three coordinate systems mentioned above. The physical meaning of the operators is also discussed. The simple applications concerning the solution of typical electromagnetic fields using three coordinate systems are brought in the forth part. It should be stressed that the presentation is not closed. It will be continually developed. In the near future we shall try to add more applications and to make the text more perfect.