104 DRIVING SYSTEMS 



the reluctance is assumed to reside in the air gap, the flux, in maxwells, 



through the armature is 



MA 

 4>i = 6.10 



a 



where M = magnetomotive force, in gilberts, due to the steady field, 



a = spacing between the armature and pole, in centimeters, and 

 A = area of the pole, in square centimeters. 

 Let the armature be deflected a distance Ax towards the pole, the flux 

 will now be 



*/ = ^^ 6.11 



a — Ax 



Now, let the armature be pulled away from the normal position a dis- 

 tance of Ax, the flux will be 



*/' = ^^ 6.12 



a -i- Ax 



The difference in flux through the armature for these two conditions is 



MJ MA IMA Ax 



A01 = (/>/ - ^," = - -— — = ~ — 6.13 



a — Ax a -{• Ax a^ — Ax^ 



This change in flux with respect to the time is 



d(^ _ IMA dx 

 dt a^ dt 



6.14 



The electromotive force, in abvolts, generated in the coil due to this 

 deflection of the armature is 



. = ^^ = ?^^x 6.15 



dt a^ 



Leaving out the steady force and the force of twice the frequency, equa- 

 tion 6.9 becomes 



U^^^ 6.16 



where / = Zmax sin co/. 



Combining equations 6.15 and 6.16 



e X IM'^m 



t Jm RiR2a^ 



6.17 



2MW^ 



Zem = p p 2 • 6.1» 



RiR2ahMT 



