THE MAUNKT1C CIRCUIT [ART. 59 



that the current is distributed uniformly over the cross-section of 

 the conductor. The length of the line of force is 2nx, so that 

 H=i x /2nx=xi/(l-n-), and B = pxi/ (2xa 2 ) . Thus, in this part 

 of the field the flux density increases as the distance from the 

 center and is represented by the straight line Oq. 



In the space inside the conductor D, a line of force of a 

 radius x is linked with the current i(x 2 b 2 )/(c 2 6 2 ) of the 

 external conductor and with the current +i of the internal con- 

 ductor, or altogether with the current i x =i(c 2 x 2 )/(c 2 6 2 ). 

 Consequently, here, the flux density is represented by the 

 hyperbola rs, the equation of which is 



The curve Oqrs gives a clear physical picture of the field dis- 

 tribution in the cable, and helps one to understand the linkages 

 which enter into the calculation of the inductance of the cable. 



The inductance of the cable is calculated according to the 

 fundamental formula (106), the complete linkages being in the 

 space between the two conductors, and the partial linkages being 

 within the space occupied by the conductors themselves. Con- 

 sider a piece of the cable one centimeter long. The permeance of a 

 tube of force of a radius x and of a thickness dx is fjidx/2xx, so that 

 the permeance of the complete linkages is, 



L C ' = (P C '= da;/27ra?Oi/2^)Ln(6/a) perm/cm., (109) 



^a 



where Ln is the symbol for natural logarithms. In this case the 

 permeance is equal to the inductance because the number of turns 

 n = l. The sign " prime " indicates that the quantities L c ' and 

 (P c f refer to a unit length of the cable. 



For the space inside the inner conductor n p = (x/a) 2 , this being 

 the fraction of the current with which the line of force of radius x 

 is linked. Hence, the part of the inductance of the cable due to 

 the field inside the conductor A is 



L/ = (fi/2it) C a (x/d)*(dx/x} =fji/Sn =0.05 perm/cm. (110) 

 J Q 



This formula shows that the part of the inductance due to the 

 field within the inner conductor is independent of the radius of the 



