PROBLEMS. 501 



where field reluctance means the total magnetic reluctance of yoke, magnet cores, and 

 pole-pieces and leakage reluctance means the total magnetic reluctance of the air paths 

 between two adjacent pole-pieces. The field reluctance is generally a small fraction of 

 the leakage reluctance so that the ratio of the two may be neglected in the above 

 expression. 



197. (a) Find the work in ergs and in foot-pounds spent in 

 magnetizing a wrought iron bar 3 inches x 3 inches x 20 inches 

 long from a neutral condition to cB = 16,000 lines per square 

 centimeter, using the tabular values of cB and 3f given in Art. 12, 

 Appendix A. (fr) Find the work in ergs and in foot-pounds re- 

 quired to magnetize a cast-iron rod of the same size from a 

 neutral condition to cB = 9,000 lines per square centimeter. Ans. 

 (a) 32.6 x io 6 ergs or 2.406 foot-pounds ; () 33.9 X io 6 ergs 

 or 2.50 foot-pounds. 



Note. Plot the c3 and &C curves from the tabular values given in Art. 12, Ap- 

 pendix A. Divide the areas between the curves and the cB axis into a number of 

 parallelograms. Calculate the area of each parallelogram and thus find the total area. 



198. A transformer core contains 96 cubic inches of the best 

 quality of transformer iron and the laminations, which are 

 thoroughly insulated from each other, are 0.014 inch thick. 

 The core, is carried through 133 magnetic cycles per second be- 

 tween the limits cB = db 3,500 gausses, by means of an alternating 

 current. Find the hysteresis loss and the eddy current loss in 

 the core both in watts. Ans. Hysteresis loss 14.7 watts ; Eddy 

 current loss 6.9 watts. 



199. The hysteresis loop (Fig. 17, Appendix A), of a sample 

 of iron for a magnetic cycle having the limits $ = =fc 12,500 lines 

 per square centimeter, has an area of 9.52 square inches. In 

 plotting the loop each inch of ordinate represents 2,000 units of 

 c& and each inch of abscissa represents 5 units of 3f. Find the 

 energy lost in 25 cubic centimeters of the iron during the mag- 

 netic cycle. Ans. 189,400 ergs. 



200. The electromagnet shown in Fig. 1 2, Appendix A, has 

 the following dimensions. The cylindrical cores, CC, are of 

 annealed wrought iron 2 inches in diameter, 8 inches long, and 

 7 inches apart from center to center. The yoke, YY t and the 



