IN CYLINDRICAL CONDUCTORS, ETC. 
83 
individual wires. In a straight single layer system the field acting on one wire is per¬ 
pendicular to the surface of the layer, bub in a single layer coil nob only is this normal 
field modified but there also exists a component of the field acting along the surface of 
the layer. The case where the number of wires in the coil is large will alone be 
considered. 
Solenoiclal Coil .—Let the mutual inductance (M) between two equal parallel coaxial 
circles of radius a and separation b be mitten 
Then* 
M = 4,-rraf (2a/b), 
( 60 ) 
/(/*) = log 4^-2 + f- 1 
(log 4/* + £)—frf - 4 (log 4 fx-U) 
fX 
~ 6 (log 4 m--M&) +. 
M 
(61) 
so long as p < 1. 
From this expression it is readily shown by differentiation and integration that the 
radial and axial components of the field at the point on the prolongation of the surface 
of a cylindrical coil distant £ from the edge are given by 
n being the number of turns per unit of length and I the current. 
When £ is very small, H N tends to the value H u — h, in which 
H 0 = 2»I log. . . 
(63) 
and is the field due to a straight strip of width b, while 
h = 2nl [f - 2 ( 1 °g 4 / x -i)-M4( lo g 4 / x -io) + ^ 5 V^(l°g 4p-ff&)...} . (64) 
Ip m P- J 
p = 2 afb. 
H t tends to the value 
H t = -i I (log 4/1-1) + * 4(log4/ l - J)-^y(log4/ i -fi) + ...} (65) 
l jv P H- V- J 
p - 2 a/b. 
To find the normal and axial components at any point on the surface of the coil, 
* Butterworth, ‘ Phil. Mag.,’ vol. 31, 216, 1916. 
N 2 
