CHAPTER XI. 



THE INDUCTANCE OF CABLES AND OF TRANS- 

 MISSION LINES. 



59. The Inductance of a Single-phase Concentric Cable. Let 

 Fig. 46 represent the cross-section of a concentric cable, which 

 consists of an inner core A and of an external annular conductor 

 D, with some insulation C between them. Let the radii of the 

 conductors be a, 6, and c, respectively. The insulation outside of 

 D and the sheathing are not shown. Let a direct current of i 

 amperes flow through the inner 

 conductor away from the reader 

 and return through the outer 

 conductor. The magnetic field 

 produced by this current links 

 with the current, and for reasons 

 of symmetry the lines of force 

 are concentric circles. The field 

 is confined within the cable, 

 because outside the external con- 

 ductor D the m.m.f. is i i=0. 



In the space between the two 

 conductors the lines of force are 

 linked with the whole current, 

 and since there is but one turn, 

 the m.m.f. is equal to i. The length of a line of force of a radius x 

 cm. is 2^xsothat the magnetic intensity isH =i/2xx, amp. turns per 

 cm., the corresponding flux density B *=fjd/2nx maxwells per sq.cm. 

 Thus, the flux density decreases inversely as the distance from the 

 center; it is represented by the ordinates of the part qr of a hyper- 

 bola. 



In the space within the inner conductor A, a line of force of 

 radius x is linked with a current i, -i(nx*/i:a 2 ) -t(*/a) 2 , provided 



189 



Fig. 46 -The magnetic field within 

 a concentric cable. 



