The Reluctance of Some Irregular Magnetic Fields

The development of the idea of magnetic reluctance is sketched, and the mathematical and experimental methods of determining it are first discussed. On the theoretical side it is the theory of complex quantities which leads to numerical results. The electric field of an electric generator is next analyzed and made to depend approximately upon the reluctance of two-dimensional magnetic fields. This study indicates as preferable the one shown in Fig. 6 at the left. The reluctance of these various magnetic fields is determined by experiments made on sheets of high-resistance metal cut in suitable forms, and by mathematical computation. These results are put into charts and formulas convenient for the use of those interested in electrical design. The results of the tests are proved to be more accurate than most of those already published. In particular, present leakage flux calculations are most in error. Of more general interest are the plates of the shape of the magnetic lines of force in the various parts of electrical machinery. In particular, Figs. 42 to 48 include some new results. The flux lines in the corners of transformers and induction motors are there shown, and the exact solution to the much-discussed sine-wave alternator problem is there given. The paper is divided into (I) Introduction, (II) Historical Development, (III) Description of Experiments, (IV) Accuracy of Results, (V) Conclusions. There are two appendices giving some mathematical details, for reference purposes.