116 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



pared with that of the coil or other external circuit. From the derivation 

 of (2), the component mmf's are proportional to the corresponding terms 

 in G, so the preceding expressions for Ge are valid only if Ge is small 

 compared with Gc{N /R). In all but exceptional cases, this condition is 

 satisfied in operation, and in release with a short circuited winding or a 

 slow release sleeve. In these cases, the effect of eddy currents is ade- 

 quately represented by a constant Ge term in (2). The exact values of Ge 

 applying are in only approximate agreement with those given by (7) 

 and (8) , as the derivation of these expressions ignores the" variation in 

 flux density along the length of the core, and the eddy current effects in 

 the armature and return path. 



EDDY CURRENTS IN RELEASE 



In normal release, the winding circuit is open, and the only effective 

 magnetomotive force is that of the eddy currents. Evidently, the field 

 in the outer layers must collapse almost instantly, while that in the 

 center of the core is sustained by eddy currents in paths whose mean 

 conductance, per line linked, is higher than that applying to a uniform 

 field. 



The relations applying to a closed path of uniform section can be 

 formulated in differential form, and the solution for a cylindrical section 

 has been given by Wwedensky. For decay from an initially uniform field, 

 the expression for the flux as a function of time is a series of exponential 

 terms with progressively smaller time constants. The first term represents 

 the most persistent part of the flux, and represents a field varying from 

 zero at the surface to a maximum at the center, comprising 69 per cent 

 of the initial field. Its time constant corresponds to an effective value of 

 Ge 35 per cent larger than that given by (7). Somewhat similar relations 

 must apply to an electromagnet, causing a time variation in the pattern 

 of the field, not only radially, as in a closed uniform path, but in the 

 longitudinal variation and in the division of the field between the leak- 

 age and armature paths. 



An experimental study of flux development and decay in relays has 

 been reported by M. A. Logan. His results agree with this discussion in 

 showing Ge in (2) to be effectively a constant, provided Ge/Gc is less 

 than 0.2, as in the operation of most relays. An empirical expression is 

 given for an effective value of Gc + Ge which provides a correction fac- 

 tor applicable for small values of Ge/Gc ■ The results for normal release 

 show the field decay to have the general character of Wwedensky 's 

 solution, and an empirical expression is given which agrees Avith ob- 

 served results. This is primarily of interest in connection with the voltage 



