102 ADVANCED ELECTRICITY AND MAGNETISM. 



Find the total magnetic flux through the middle part of the 

 magnet. Ans. 24,972.8 maxwells. 



Note. In this case the net magnetizing force, &C, at the middle of the bar is a 

 demagnetizing force, and the flux due to &C is subtracted from 



8. A transformer has a sheet iron core of which the uniform 

 sectional area is 120 square centimeters. The mean length of 

 the magnetic circuit formed by the core is 100 centimeters. How 

 much current must be passed through a winding of 500 turns of 

 wire to produce a magnetic flux of 1,767,000 lines through the 

 core? Ans. 3.88 amperes. 



9. How much flux will be produced through the wrought iron 

 core, specified in problem 8, by a current of 8.2 amperes through 

 the 500 turns of wire? Ans. 1,920,000 lines. 



10. The magnetic circuit of a dynamo consists of wrought 

 iron (in armature core and in field cores), cast iron (in field yoke 

 and pole pieces), and air gap. The wrought iron portion is 50 

 centimeters long and 120 square centimeters in sectional area, 

 the cast iron portion is 40 centimeters long and 220 square centi- 

 meters in sectional area, and the air portion is 2.5 centimeters 

 long and 300 square centimeters in sectional area. How many 

 ampere-turns are required to force 1,600,000 lines of flux through 

 this circuit, ignoring magnetic leakage? Ans. 12,100 ampere- 

 turns. 



Note. On account of magnetic leakage the magnetic flux through field yoke, 

 field cores and pole pieces is larger, sometimes very much larger, than the flux which 

 flows across the air gaps and through the armature core. Therefore a slightly 

 greater magnetomotive force is required to overcome the magnetic reluctance of 

 field yoke, field cores and pole pieces than would be required if the magnetic leakage 

 were zero. 



11. How much magnetic flux would be forced through the 

 magnetic circuit specified in problem 10 by a magnetomotive 

 force of 13,500 ampere-turns? Ans. 1,723,000 lines. 



Note. This problem is to be solved by calculating a series of values of ampere- 

 turns for various assigned values of flux. These results are to be plotted. The 

 flux corresponding to 13,500 ampere-turns may then be taken from this curve. 



