﻿Self and Mutual Induction of Coaxial Coils. 585 



Also 



(28) 



by integration by parts. 



Performing the last integral of (2S) by expanding 

 (1 — a- 2 sin 3 0) _ * in ascending powers of a*, and integrating 

 term by term, 



7T f, 4 5/1.3'- 5 2n-lV« a »\ , ooS 



8. The mutual induction between two semi-infinite co- 

 axial cylinders of radii a and b, external to each other and 

 with their ends in contact, is 



m=*Tra\(a 2 +b 2 )E-(a 2 -b 2 )K\, . . (30) 



the linear winding density being unity, and the modulus of 

 E and K being b/a, with a > b. 



The mutual induction between a solenoid of radius a and 

 a solid coil of radius b (a>&) with their ends in contact is 



n h = f,7ra\ b )(a 2 + b 2 )E-(a 2 -b 2 )K\db, . (31) 

 • 

 which on applying the reduction formula? becomes 



When b = a, 



1 , 4 /17 3 \ /0 .,, 



mi =m 2 — 3^ (y "~ 9"! )• • • • ^) 



The mutual induction between a solenoid of radius b and 

 a solid coil of radius a (a>b) with their ends in contact is 



C a 



■m 3 = mi 2 H"1 mda 



3 /) 4 "1 



-|^(«+«i)}- • (34) 



