12 THE MAGNETIC CIRCUIT [ART. 7 



magnetic materials. For magnetic materials /* is considerably 

 larger than for non-magnetic, and varies with the field strength. 

 In calculations either reluctivity or permeability is used, according 

 to the conditions of the case and the preference of the engineer. 



The student has probably heard before that the permeability of 

 air is assumed equal to unity. The discrepancy between this com- 

 monly accepted value and the value 1.25 given above, is due to a 

 different unit of magnetomotive force, called the gilbert, which is 

 sometimes employed. The author considers the gilbert to be 

 of doubtful utility, for reasons stated in Appendix II ; hence no 

 use is made of it in this book. 



Prob. 10. Assuming the value of /* = 1.257 to be given, check the 

 value of /=3.19 in the English system, and also the values of v in the 

 metric and the English systems, as given above. 



Prob. 11. In prob. 4 the reluctance of a ring was 20.7 rels. If the 

 cross-section of the ring is 120 sq. mm., what is the average diameter of 

 the ring? Ans. 9.9 cm. 



Prob. 12. How many ampere-turns are required to establish a flux 

 of 47 kilolines in a ring of rectangular cross-section, made of non-magnetic 

 material; the radial thickness of the ring is 8 cm., the axial width 11 cm. 

 and the average radius 16 cm? Ans. About 43 kiloampere-turns. 



Prob. 13. How many ampere-turns would be required in the preced- 

 ing problem for the same flux if the ring were made of iron, the relative 

 permeability of which (with respect to air) is 500? 



Ans. 86 ampere-turns. 



7. Magnetic Intensity. In order that the student may better 

 appreciate the significance of the concept of magnetic intensity, 

 it is advisable to refresh in his mind the corresponding quantity 

 used in the elect-ric circuit, viz., the electric intensity. Namely, in 

 problems on the electric and the electrostatic circuit it is some- 

 times desirable to consider not only the total voltage, but also 

 the voltage used up or balanced per unit length of the path along 

 which the electricity flows or is displaced. This quantity, the 

 rate of change of voltage along the circuit, is known as the electric 

 intensity, or the voltage gradient. It is denoted by F (see the 

 Electric Circuit), and is measured in volts per linear centimeter. 

 When the voltage drop is uniform along a conductor or a dielectric, 

 F=E/l, where E is the voltage between the ends of the part of the 

 circuit under consideration, and I is the corresponding length. 

 When the voltage drop is not uniform, F is different for different 

 points along the path, and for each point F=dE/dl. 



