THE DEMAGNETIZING FACTORS FOR CYLINDRICAL 



IRON RODS. 



By C. L. B. Shuddemagen. 



Presented by B. O. Peirce, AprU 10, 1907. Received June 25, 1907. 



Outline of the Subject, 



It has long been known that when an unmagnetized iron bar is 

 placed in a fixed magnetic field H' and thereby becomes magnetized, 

 the actual force H within the iron is not so great as the original per- 

 manent magnetic force at the same point before the iron was introduced. 

 The vector difference Hi, between the original force and the actual 

 force resulting after the iron is brought in, is called the " demagnetizing 

 force" due to the magnetism which has been induced in the iron. An 

 original uniform field does not in general induce a uniform demagneti- 

 zing field within a piece of iron ; in fact, it is commonly accepted that 

 there is only one practical exceptional case : an iron ellipsoid placed 

 so that a given one of its axes is parallel to the direction of the original 

 uniform field. In this case the demagnetizing force for a given ellipsoid 

 with a given axis parallel to the field is simply proportional to the 

 resulting uniform intensity of magnetization /; and the proportionality- 

 factor N is found by theory to depend only on the dimensions of the 

 ellipsoid, that is on the semi-axes a, b, and c. Moreover, when the 

 ellipsoid is a body of revolution, so that b = c, then we have a simple 

 formula expressing N as depending solely on the value of the ratio a/b. 

 This AT" is commonly called the "demagnetizing factor" for the 

 ellipsoid. 



Lord Rayleigh ^ first pointed out how from a knowledge of N a 

 hysteresis curve obtained for an iron ellipsoid of revolution and plotted 

 on the B vs. H' plane, could be " sheared back " into the limiting hys- 

 teresis curve for an ellipsoid of the same cross-section, which would be 

 approached as the length of the axis which lies parallel to the field 

 grows longer and longer. The same process is evidently applicable to 

 a simple magnetization curve obtained by letting the applied field U' 



1 Phil. Mag., 22, 175-183 (1886). 



