CHAP. XI] INDUCTANCE OF TRANSMISSION LINES 195 



coincide at infinity, because the distance AB between their a 

 infinitely small as compared to their radii. Hence, the two cur- 

 rents in the cylinders cancel each other, and the combination of 

 the two component systems is magnetically identical with the 

 given loop. 



In a medium of constant permeability, the resultant magnetic 

 intensity H, produced at a point by the combined action of several 

 independent m.m.fs., is equal to the geometric sum of the intensi- 

 ties produced at the same point by the separate m.m.fs. 1 This 

 being true of the intensities, the component flux densities at any 

 point are also combined according to the parallelogram law 

 because they are proportional to the intensities. Hence, the 

 resultant flux can be regarded as the result of the superposition 

 of the fluxes created by the component systems. 



The field produced by the system A consists of concentric cir- 

 cles, the flux density outside the conductor A being inversely pro- 

 portional to the distance from the center of A (curve qr in Fig. 46). 

 The field created by the system B consists of similar circles around 

 B, and the field shown in Fig. 47 is a superposition of these two 

 fields. Thus the resultant field intensity H at a point P is a 

 geometric sum of 



#1=1/2*7-!, ....... (115) 



and 



....... (116) 



HI and H 2 being perpendicular to the corresponding radii vectors 

 TI and r 2 from the centers of the conductors to the point P. The 

 directions of H\ and HI are determined by the right-hand screw 

 rule. Since H\ and H 2 are known in magnitude and direction at 

 each point of the field, the resultant intensity H may also be deter- 

 mined. 



To deduce the equation of the lines of force in the resultant 

 field, we shall express analytically the condition that the total flux 

 which crosses the surface CP is equal to zero, provided that C and 

 P lie on the same line of force. This total flux may be considered 



1 This principle of superposition can be consi-1. n ,] ,) as an experimental 

 fact; (6) as an immediate consequence of the fact that in a medium of constant 

 permeability the effect* are proportional to the causes; (c) as a conscqu. ncr 

 : .lace's law dH - Const. X i da sin 0/lOr 1 , according to which th t..i.,i 

 fi-M mt< M-itv is regarded as the sum of those produced by the infinitesimal 

 elements of the current, or currents. 



