Transforming the Expression of the Integral of a Vector Field Curl over a Cylindrical Surface into Another Surface Integral without Differential Operators

摘要

The integral of a curl of a vector field, defined in the paper, and extended over the lateral surface of a cylinder, will be transformed into a surface integral extended only over the bases of the cylinder, not containing differential vector operators. The transformation will be carried out using only the general formulae of vector analysis without resorting to other proofs of the field theory. The type of integral is an interesting one because it permits to obtain directly, without physical considerations, only mathematically, certain formulae useful in physics.