THE MAGNETIC CIRCUIT ELECTROMAGNETS 29 



provided under the magnetizing coils and in the yoke to carry the 

 leakage flux in addition to the useful flux. The leakage factor 

 is always greater than unity, and the product of the useful flux 

 by the leakage factor will be the total flux to be carried by 

 certain portions of the magnetic circuit enclosed by the exciting 

 coils. 



8. Tractive Force. The tractive effort, or the tension which 

 exists along the magnetic lines of force, is one of the effects of 

 magnetism which it is necessary to calculate, not only in electro- 

 magnets for lifting purposes, or in magnetic clutches or brakes, 

 where this is the most important function of the magnetism; 

 but also in rotating electric machinery, where decentralization of 

 the rotating parts may lead to very serious results owing to the 

 unbalancing of the magnetic pull. 



MAXWELL'S formula is, 



B z 

 Force in dynes = gA (14) 



where A is the cross-section in square centimeters of a given area 

 over which the flux density, B, is assumed to have a constant 

 value. 



This formula can be used to calculate the pull between two 

 parallel polar surfaces when the air gap between them is small 

 relatively to the area of the surfaces. The engineer desires to 

 know the pull in pounds exerted between the two surfaces, and 

 since 1 Ib. = 444,800 dynes, the above formula can be written, 



B 2 



pull, in pounds per square centimeter = -M IQQ QQQ 



or 



B 2 



pull, in pounds per square inch = 



In both of these formulas the density, B, is expressed in gausses 

 (i.e., in C.G.S. lines per square centimeter). 

 If B,, stands for lines per square inch, then, 



B 2 



pull, in pounds per square inch = 72 X 10 6 



If the density is not constant over the whole surface considered, 

 the area must be divided into small sections, after which a 

 summation of the component forces can be made. In averaging 

 the density to get a mean result, it is obviously not the square of 

 the average density that must be taken, but the average of the 



