54 PRINCIPLES OF ELECTRICAL DESIGN 



because the large cross-section necessary to keep the flux density 

 within reasonable limits would lead to an unnecessary and 

 wasteful increase in the weight of the copper coils. 



Applying formula (16) of Art. 8, page 29, the pull, expressed 

 in terms of the air-gap density is 



p = _2AB*_ 

 1,730,000 



where B is in gausses, and A is the area of one polar face, expressed 

 in square inches. Thus, 



200 - WE * 

 ~ 1,730,000 



whence, 



13,150 

 w = g- (34) 



This relation between size of pole face and the air-gap density 

 must exist if the pull of 200 Ib. is to be obtained, but the density B 

 can be varied within wide limits. It is obvious that high values 

 of B are advantageous in so far as they reduce the weight and 

 cost of the iron in the magnet; but since the initial air-gap length 

 remains constant, the necessary ampere-turns will increase 

 almost in direct proportion to any increase of B. The economical 

 value of the flux density, J5, cannot be immediately determined; 

 and although formulas for minimum cost can be developed, they 

 become unwieldy and unpractical when all the important 

 factors are taken into account. On the other hand, if all deter- 

 mining factors including such items as cooling surfaces and 

 magnetic leakage are not taken into consideration, the formulas 

 are very inaccurate and not of general application. It is very 

 interesting to develop approximate formulas for use in arriving at 

 the economical dimensions of any particular type of electro- 

 magnetic apparatus, and the reader may learn much by trying 

 to put the various, and frequently conflicting, requirements in the 

 form of a mathematical equation; but we shall follow here the 

 method adopted by a large number of experienced designers, 

 which consists in trying what seems a probably value for one of 

 the unknowns, and then checking results by assuming a larger 

 and a smaller value for the unknown quantity. 



Since very low values of B will lead to great weight of iron, 

 and very high values will lead to an increased weight of copper, 

 it is safe to assume that B will not be less than 5,000 or more than 



