622 BELL SYSTEM TECIINLCAL. JOURNAL 



list of electron tubes for l'M5, nine were developed at the Bell Telephone 

 Laboratories. 



APPENDIX I 



Resonators 



In thinkin<f about resonators it is imjM)rtant in order to avoid confusion 

 to keep a few fundamental ideas in mind. One of the most important is 

 that we must not use the notion of scalar potential in connection with fluc- 

 tuating magnetic fields. Electric fields produced by fluctuating magnetic 

 fields cannot be derived from a scalar potential, and in the presence of such 

 fields to speak about the potential at a point is hopelessly confusing. 



The idea of voltage as the line integral of electric field along a given path 

 between two points is useful, but it must be remembered that the voltage 

 depends on the path chosen. Consider, for instance, an ordinary 60-cycle 

 transformer with the secondary wound of copper tubing. For a path from 

 one secondary terminal to the other through the center of the tubing the 

 voltage (integral of field times distance) is zero. For a path between ter- 

 minals outside of core and coil, the voltage between terminals is d\l//dl, 

 where i/' is the magnetic flux linkage of the path and the coil, counting each 

 line of force as many times as the path encircles it. 



If resistance drop is neglected the work done in moving a charge through 

 a conductor is zero. The line integral of an electric field around a closed 

 path is d\l//dt. If part of the path is through a conductor, or through a 

 space where there is no electric field, the voltage along the rest of the path 

 (as between portions of the conductor) isdip/dt. For paths linking different 

 amounts of flux, the voltage will be different. In the case of low frequency 

 transformers, all paths linking the terminals and lying outside of the core 

 and coil link practically the same amount of flux, and there is little am- 

 biguity about the voltage. In reflex oscillators the electrons travel from 

 one field free region to another along a certain path and this determines 

 the path along which the voltage should be evaluated. 



To review: the voltage between two points is the integral of the field along 

 the path times distance, and refers to a certain path. If the path begins 

 and ends in a lield free region, the voltage is d\p/dt, where \p is the magnetic 

 flux linking tlie chosen path and a return path through the field free region. 



To this should be added that high frequency currents and fields penetrate 

 the surface of metals only a fraction of a thousandth of an inch in the 

 centimeter range, so that the interior of a conductor is field free, and fields 

 inside of a metal enclosed space cannot produce fields outside of that space 



"* The electric field can, of course, be derived from a scalar and a vector i)otential. 



'^ .Vs an exani])le, for copper the field is reduced to (1/2.72) of its value at the surface 



