A New Vector Analysis Approach to the Calculation of the Magnetic Field Strength of a Solenoid

A new approach to the general formula of the magnetic field strength produced by a solenoid having the cross-section of arbitrary shape is presented. The new approach is based on a theorem of vector analysis established by the author and presented below. The obtained expression is of a simpler form than the usual ones; however, the numerical computations have shown the accuracy of the results of the same order of magnitude as that of the application of the Biot-Savart-Laplace formula. Moreover, the derived formula contains, separately, the components of the magnetic field strength, namely, the Coulombian and non-Coulombian ones, that is very interesting from a theoretical point of view. Consequently, in addition, the derived formula allows the direct introduction of the magnetic polarization and of the magnetic field state quantities.