The electromagnetic field of a circular parallel plate capacitor excited by an AC current and AC voltage supply

Abstract This study investigates the electromagnetic field (EMF) distribution of an ideal circular parallel plate capacitor excited by a time-harmonic power source. Considering the lead wire and capacitor as a charged whole, we formulate the boundary value problems of the Helmholtz equation for the EMF in the lead wire space and capacitor space, respectively. First, we solve for the EMF generated by the total current in the lead wire space of an AC current. Following this, we solve for the EMF boundary value problem of a capacitor filled with linear, uniform, isotropic, and non-magnetic lossy dielectric under an AC current excitation, using the continuity of the total current as a basis. Second, the EMF distributions in the capacitor space and the lead wire space under an AC voltage excitation are provided, following the principles of the generalized Helmholtz theorem. Third, the EMF distribution is discussed when the electromagnetic ‘standing-wave phenomenon’ occurs in the ideal dielectric capacitor, and identify the ‘resonance phenomenon’ and the ‘current-stopping phenomenon’ of the capacitor's EMF when excited by an AC current and AC voltage, respectively. We also present the corresponding ‘resonance frequency’ and ‘current-stopping frequency’. Finally, we explore the quasi-stable solution of the capacitor's EMF under low-frequency condition and the static solutions of the electric and magnetic fields under DC excitation and static voltage excitation. Our findings suggest that the existing formula for the capacitor's EMF approximates our analytical solution under quasi-stable condition.