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BELL SYSTEM TECHNICAL JOURNAL 



in the shape of a sphere concentric with the center of the wire and 

 passing through its ends. Thus we could calculate the radiated power 

 from an appropriate distribution of magnetic currents over this sphere 

 but in this case such a procedure would involve more difficult inte- 

 grations than the usual method. 



Before considering the more general case of radiation from a semi- 

 infinite coaxial pair let us assume that the radii of the two conductors 

 are nearly equal. We have seen that in applying the Equivalence 

 Principle we need take into account only the magnetic current sheet 

 over the open end of the pair. In the present instance this sheet is 

 merely a circular loop of magnetic current equal to the voltage V 

 between the ends of the conductors. If we were to treat in the same 



Fig. 8 — A vertical antenna and a cross-section of an imaginary sphere 

 passing through the ends of the antenna. 



manner a condenser made of two parallel circular plates, we should 

 come to the conclusion that it is also equivalent to a magnetic loop 

 around its periphery. Thus in both cases the radiated power is the 

 same. But the power radiated by an electric doublet is known to be 

 {40Tr^PP)/\'^ watts where I is the amplitude of the electric current, / the 

 length of the doublet and X the wave-length. In applying this formula 

 to a condenser it is better to express it in terms of the voltage V 

 across the condenser and its area S. The capacity of the condenser is 

 C = 5/(367rl0"/) farads and / = wCV = SV/60\l amperes. Hence 

 the power radiated by the condenser is (ir^S^V^)!90\* watts. This is 

 also the approximate power radiated by the coaxial pair if we interpret 

 5 as the cross-sectional area of either conductor. 



