Graphical Determination of Magnetic Fields Theoretical Considerations

Three papers on the general subject, ``Graphical Determination of Magnetic Fields,´´ are being presented simultaneously to cover three phases of the subject: 1. Theoretical Considerations, 2. Comparison of Calculations and Tests, by E. E. Johnson and C. H. Green, 3. Practical Applications to Salient-Pole Synchronous Machine Design, by R. W. Wieseman. In the following paper, which is the first of this series, the authors have reviewed the history of the subject, hare briefly stated the ordinary rules for plotting magnetic flux in air and in current-carrying copper, have developed additional rules for checking the accuracy of field plots, and have given theoretical methods for mathematically calculating the distribution of field in certain cases commonly encountered in practise. The authors have called attention to the great value of the mathmatical work by the German engineer, Rogowski, and the graphical methods by the French engineer, Lehmann. These German and French articles contain the only extensive practical applications of the plotting of magnetic fields in current-carrying regions with which the present authors are familiar. Since it is much more difficult to plot fields in current-carrying regions, and since the majority of readers are less familiar with this phase of the subject, the greater part of the first paper, ``Theoretical Considerations,´´ is devoted to a study of such fields.