COEFFICIENTS OF SOLENOIDS. 19 



L =:4:7Tn/ X Area of Cross Section x Length 



wliere n is the number of turns per unit length ; for solenoids 

 of any length, it will be shown that 



i:=4-M-xArea of Cross Section x Length x 8. 



where S can be tabulated once for all as a function of angular 

 aperture or of the ratio of diameter to length of the solenoid. 

 When once the values of 8 are known, the calculation is greatly 

 facilitated, as the rest of the operation is a simple multiplication. 

 § 12. It has already been shown in § 7. that the mutual 

 inductance of coaxal solenoids 



3I=A7:nn'Aa [/,-/,-/,+ 7J (7) 



where 7=2[^(^-|^ -F^J^^i +pv.-^i + -2\^'^ ~~ ^''^"^^^vJ ^^^^ 



The case which deserves special attention is when the radii and 

 the lengths of the solenoids coincide; i.e., when d = o, A=a, 1=1', 

 11 = 71,'. In this special case, 31 is transformed into L 



For c = 2l, pv = c., , or v = cü. and p'v = o. 



I- . . «-— Z- , . 



e^-f.= --~.{e.,-e.^, (ii-c^ = —-^—-{Ci-^ù 



(.by ^ 



1 câ~P , . ,o e.2 — e. a" 



- 3 «- ^ -' ^ ' 61 — 63 a^+l- 



For c = o, pv=c^=e., , or u = co^^ = co. and p'v = o. 



Thus 1^=1.= ^^'-'^-^'^^-'^ co^-^-e^:^ 



L=Z^ = ^^, (14) 



Utilizing the relation 

 K 



ye^ — e. y 61 — 63 



