On the Induced Current and Energy Balance in Electronics

With a given specification of the space-charge density and velocity functions for a general electron-tube system, the balance of instantaneous rates of energy change between the space and the external circuits has been derived here from Green's theorem. It is shown that the external currents can be completely accounted for by the changes brought about by moving charges and changing field intensity in space. The ordinary concept of current as the rate of direct transfer of charges represents the limiting case of this theory at low frequencies. The induced current for steady fields can be calculated simply by knowing the electrostatic field caused by a given electrode at unit potential, with all the other electrodes grounded, and the space-current density function. It is also shown that a direct-current source can supply power only when there is a direct flow of charges between the space and the electrode to which the source is connected. Net alternating-current power, however, can be exchanged between the space and the external circuits even in the absence of direct transfer of charges. A number of ultra-high-frequency phenomena can be qualitatively explained by the theory.