Radial and Axial Components of Magnetic Force. 195 

 It will be found that 



(a) X = 



2 [V = "( - 1? OS^-T** 1 n 



7 v r 



03) Z * 27r r r"2(S-T) 



Since 7i(S - T) = the number of turns per unit of length, = N (say), 

 the defect of Z from 47rNy depends on the importance of the terms 

 under the sign 2. For the region near the equatorial plane of an 

 infinitely long solenoid these terms become vanishingly small. 



The series under the sign 2 are convergent, though not very rapidly 

 so if S is nearly as large as r or /. 



Case II. 



Expressions for the region near one end of a long solenoid where 

 r < T and r > S. 



In this case 



(7) X = 



!_./ u>v kj 



(2^ + 2) ! -Q^;-TP^; 



r ff 



(8) Z = 2= 



1 1 



From (8) it is easy to deduce the fact that in the plane of one end 

 of an infinitely long solenoid the axial component is constant and equal 

 to 27rNy, i.e., half its value for the equatorial region of the same coil. 



VOL. LXIV, 



