Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

486 FREQUENCY MODULATION, Volume IIII.General Field-Theory TreatmentWhen electrons are injected into cavities or systems with distributedconstants, it is convenient to be able to calculate the resultingchanges in frequency in terms of the electromagnetic field quantitiesand the forced electron convection current, rather than in termsof currents induced in a circuit containing lumped constants as wasdone in Section I.This can be done quite simply with adequate accuracyby means of a perturbation method.The electromagnetic field in a region of space entirely enclosed bya perfectly conducting surface will be given by a solution of Maxwell'sequations for which the tangential component of electric field at thesurface vanishes. When the field quantities are expressed in the meterkilogram-second3 system of units, these equations are:Curl H = J + zEDiv H =Curl E = -tiHDiv E = P /e.(54a)(54b)(54c)(54d)In obtaining solutions of (54), it is convenient to reduce the numberof equations by expressing^ and H in terms of the scalar potentialand the vector potential A by means of the relationsE = — A — grad whereWhen so expressed, E and H automatically satisfy (54b) and (54c)and we are left with the problem of solving the equationsV•V A — e/iA = — pj + fie grad + grad div AV 2