MAGNETISM AND ELECTROMAGNETICS 



65 



and is equal to the m.m.f. divided by the total reluctance; and 

 the m.m.f. is 



M = $31 = 3>m y + $3l c + $3l p + $91, + $a a 



= M y + M c + M p + M, + Ma, 



where M y is the part of the total field m.m.f. required to drive 

 the flux through the yoke, etc. 



The m.m.f. M g required to drive the flux across the air gaps is 

 sometimes as much as 80 per cent of the total m.m.f. 



(5) Determine the reluctance of the ring in Fig. 54 made up of 



FIG. 54. 



three parts of lengths h, 1 2 and k cm. respectively and sectional 

 areas A 1} A 2 and A 3 sq. cm. and permeabilities /zi, ju 2 and ^3. The 

 m.m.f. of the solenoid is M. 



The reluctance of section (1) is 3li = 



the reluctance of section (2) is ^ = 



the reluctance of section (3) is 91 3 = 



M 



the flux through section (1) is $1 = 5^- ; 



M 

 the flux through section (2) is <t> 2 = s^- ; 



