CONCENTRIC COILS. 533 



The factor N represents the total number of turns of the outer 

 solenoid, and g the flow of force produced in the inner solenoid 

 by a current equal to unity. 



553. CONCENTRIC COILS. Let us in like manner consider 

 two concentric coils composed of several layers of wire closely 

 pressed together, so that in unit surface of a meridian plane, the 

 number of wires is respectively n\ and n y For layers of the 

 thicknesses dr^ and dr^ and of lengths equal to unity, the number 

 of wires will in like manner be n\dr v and n\dr y We shall have then 



for each coil, the integral being extended to the entire thickness. 

 Denoting the extreme radii by y l and x- for the first coil, and by 

 y 2 and x 2 for the second, we get 



If we disregard the effect of the ends, the value of the co- 

 efficient of mutual induction will be 



(51) M = N-= ***&& - *J (y\ - 



When the layers of the two coils are in contact, we may put 

 # 2 = y l =y. If we wish to arrange the intermediate radius so that 

 the coefficient M is a maximum, we must satisfy the condition 



= - i+- + -i 



y r 



Since the latter member of this equation is less than unity, the 

 outer coil must not be so thick as the inner one. 



