798 EXPLORATION GEOPHYSICS 



Rg -^ — = reluctance of two air gaps in series below the armature for a dis- 

 ' placement s. 



4>i = magnetic flux through upper magnet. 

 <t>2 = magnetic flux through lower magnet. 

 <pa = magnetic flux through armature. 

 Fa = magnetomotive force created by the current in the armature coil. 



The application of Kirchoff's laws to the two meshes of Figure 487 yields 



F — </>! I Rg i + i? I + 0O i^o 



F (R.^ + R + ZRa'^ 

 (^R,^ + R + Ra'^(^Ra^ + R + Rc.)-Ra' 



F(R/-^+R + 2Ra') 

 (P.^+R + Ra^ (R,^-^ + R + Ra^-Ra' 



Whence 



2FR.-f 



(P.^^+R+Ra^ (p.^-j^ + R + Ra^-RJ 



The total kinetic energy of the electromechanical system is given by 



T = y2Vir-+Tei + Te2 + Tez (153) 



where 



m= combined mass of magnets and springs (moving parts). 

 Tel = energy stored in permanent magnetic field. 

 Te2 = magnetic energy due to current i induced in the armature coil. 

 7" 63 = magnetic energy due to reaction of the current i on the permanent magnetic 

 field. 



If it is assumed for simplicity that the magnetic energy is contained only within 

 the air gaps and the magnetic material and not in the space outside, 



or 



r.i=[,^x^(7? + 7?,-^)+^„==i?. + 0/(i? + 7?,-^)] 'J^ = Tei(s) (154)* 



It may be shown by using Ampere's law (magnetomotive force = 0.4 tt x ampere 



* In setting up this equation and various subsequent equations, it is assumed that 

 T, V, and D are expressed in joules; .s in centimeters; s in centimeters per sec; q in 

 coulombs ; g = J in amperes ; m in grams x 10"' ; Vm in dynes sec.^ per cm x 10'' ; 

 C in farads ; r in ohms ; L in henrys ; / in dynes x 10^', e in volts ; F in gilberts ; R in 

 charge^ over mass x length" or sec. per ohm ; in maxwells. 



