8 BELL SYSTEM TECHNICAL JOURNAL 



from the field which determines the radiation, and explains the fact 

 that radiation may usually be neglected in calculating the distribution 

 in the network.'^ 



To examine the radiation field, consider a point P at such a distance 

 from the system that 2Tr{r/X) is very large. Choose any point in the 

 system as the origin and write ro as the distance from the origin to the 

 point P, and r' the distance from the contributing element P' to the 

 origin. Then 



r = To - (r'-n), 



where n is the unit vector parallel to ro and 



-!0))-|| p —iui-Q 



■r- u-e'"^''-"^dv = ^ J, 



^0 J ro 



^ = ^ 



curl A 



which determines H. 



Instead of calculating E from the formula 



— grad $ A, 



we make use of the fact that in the dielectric 



iooE = curl H, 

 whence 



E = - IH-n']. 



The interpretation of these equations is that in the radiation field E 

 and H are equal, are in phase and are perpendicular to each other 

 and to the vector ro. Consequently the radiation vector S is given by 



S =^H^ 



and the radiation is everywhere outward. 



These formulas can be used to calculate the radiation in terms of 



the current distribution alone, and the charge distribution does not 



appear explicitly. 



^ Conversely the field in the immediate neighborhood of the system is no criterion 

 of the radiation field or the radiating properties of the system. This fact is not 

 always kept in mind by radio-engineers. 



