260 Mr. H. A. Rowland on Magnetic Distribution. 



p+dp = 



(, + RrfL)* 



p+RdL-f 



dh 



whence 



and 



, - Ae 2rL — 1 



P = V/RR Ae 2rL +1 



(1) 



To find Q', we have 



whence 



and 



dQ 1 



Q'= 



,_Q'p 



R' 



P«*L, 



A + l 



(A6 rL + e- rL ) 



-rL\* 



Of 



_ Q'pAL _ CAL 



R' 



r A+T^- 



-rL 



(2) 



(3) 



When L is very large, or s = v / RR / , we have 



Q' = 0^' and Q|.=C/-AI«fS 

 in which L, is reckoned from an origin at any point of the rod. 



These equations give the distribution on the part outside the 

 helix ; and we have now to consider the part covered by the helix. 

 Let us limit ourselves to the case where the helix is long and thin, 

 so that the field in its interior is nearly uniform. 



Fie. 1. 



As we pass along the helix, the change of magnetic potential 

 due to the helix is equal to the product of the intensity of the 

 field multiplied by the distance passed over ; so that in passing 

 over an elementary distance dy the difference of potential will be 

 iQdy. The number of lines of force which this difference of po- 



d" 2 Q' 

 * This could have been obtained directly from the equation ~l. =QV 2 , 



and Q' e from the equation Q' e = -=- AL. 



dU 



