THE MAGNETIC CIRCUIT ELECTROMAGNETS 15 



3. Effect of Iron in the Magnetic Circuit. Consider a toroid 

 or 'closed anchor-ring of iron of uniform cross-section A square 

 centimeters, wound with SI ampere-turns evenly distributed. 



Applying the fundamental formula $ = m.m.f. X P, we have, 



$ = QAirSI X ~y 



in which I is the average length of the magnetic lines, or irD 

 centimeters, where D is the average diameter of the ring. 



Thus, if A* is known, the flux in the ring can be calculated for 

 any given value of the exciting ampere-turns SI. Since ju is a 

 function of the density B, and B = 3>/A it may be convenient to 

 put the above expression in the form 



B = 0.47r7 y 



Also, since m.m.f. (in gilberts) = HI 



B = HI X | 



D 



whence V jf' which explains why the permeability is sometimes 



referred to as the multiplying power of the iron. Thus, for a 

 given value of H, the magnetic flux in air will be H lines per 

 square centimeter of cross-section, but if the air is replaced by 

 iron, it will be pH or B lines. This accounts for the fact that 

 H (the magnetizing force, or m.m.f. per centimeter) is also 

 referred to as the intensity of the magnetic field, or magnetizing 

 intensity, and, as such, expressed in gausses. This conception 

 is liable to lead to confusion of ideas; but it is well to bear in 

 mind that, in air and other "non-magnetic" materials, the 

 numerical value of B is the same as that of H. 



For a given magnetizing force H (or exciting ampere-turns per 

 unit length of circuit) the value of the permeability, /A, varies 

 considerably with different kinds of iron; it also depends on the 

 past history of the particular sample of iron, and will not be the 

 same on the increasing as on the decreasing curve of magnetiza- 

 tion-, as indicated by the curve known as the hysteresis loop. 

 For the use of the designer, careful tests are usually made by the 

 manufacturer on samples of iron used in the construction of 

 machines, and curves are then plotted, or tables compiled, based 

 on the average results of such tests. Curves of this kind have 

 been drawn in Figs. 2 and 3. The B-H curves of Fig. 2 should 

 be preferred when the C.G.S. system of units is used in the 



