MAGNETIC MEASUREMENTS AT LOW FLUX DENSITIES 45 



It thus appears that the Rayleigh hysteresis loop impHes a definite 

 relationship between the variation of permeability with // or B, as 

 calculated from bridge measurements of inductance at various coil 

 currents, and the observed hysteresis resistance. Efforts to judge as 

 to the general applicability of the Rayleigh form of loop by means of 

 such a-c. bridge comparisons have indicated fairly good agreement for 

 most materials, but occasional deviations as high as 40 per cent.* 

 Best agreement is generally found in well annealed and unstressed 

 materials, while deviations are found in such materials as compressed 

 dust cores. In such comparisons, the anomalous residual loss, vari- 

 ously termed magnetic viscosity, and after-effect, is excluded. This 

 additional loss will be discussed below. 



Mutual Effect of Rayleigh Hysteresis and Eddy Current 

 Shielding in Sheet Material 



Taking the above equation as the simplest general representation of 

 hysteresis loops at low flux densities, it now becomes necessary to 

 review the previous work with additional refinements to include the 

 effects of hysteresis upon eddy currents, and of eddy currents upon 

 themselves, and upon hysteresis. Thus the fact that B varies ac- 

 cording to a hysteresis loop equation rather than directly with H 

 modifies the eddy current loss somewhat. Also, eddy currents set up 

 magnetizing forces within the magnetic material which more or less 

 neutralize that applied by the coil winding, and thus effectively shield 

 the inner parts of magnetic laminations of wires. Such eddy current 

 shielding reduces the total flux in the core, thus decreasing the in- 

 ductance and loss resistance observed at higher frequencies. 



The fundamental differential equation giving the relation between 

 B and H at a. point x distant from the median plane of a magnetic 

 sheet is^ 



^ - A ^ . (30) 



For the simple case of constant permeability in which B = fxoH, 

 this equation has been solved by Heaviside, J. J. Thomson,^" and 

 others. 



For the case in which B is given by Rayleigh's equation (25), the 

 solution is very much involved. The variable permeability gives rise 



8 E. Peterson, B. S. T. J. 7, 775 (1928). 



^ E.g., Russell, "Alternating Currents," Vol. I, p. 487 (1914). 



^"Electrician 28, 599 (1892). 



