Abridgment of magnetic leakage and fringing flux calculations

The object of this paper is the development of an empirical method of determining leakage and fringing fluxes in an electromagnetic system. Certain assumptions are made; namely, (a) the reluctance of the iron parts of the magnetic circuit are negligible as compared with that of the air-gaps; (b) the leakage and fringing components of the flux follow paths of convenient geometric shape. Formulas are derived for leakage and fringing fluxes as percentage of the main flux which crosses the gap from the pole face, for two cases, (1) a pole core of circular section and (2) one of rectangular section. Calculations of these fluxes, in percentage of the main flux, are given over a convenient range of gap lengths, coil lengths and distance of coil from pole face. It is seen that both leakage and fringing depend to a considerable extent on all these factors. Calculations are made to determine the flux density at various points along the core length and these show a wide variation in density in accordance with the dimensions of the magnetic circuit. An experimental check was made of certain of the calculated results, and the agreement obtained was as close as could be expected, the derivation being within the limits of error of observation. The paper is not a complete discussion of the subject but it is hoped to develop it still further in a subsequent paper.