Magnetic response of planar dielectric rings

•The magnetic response of a planar dielectric ring of arbitrary width to an external time-harmonic magnetic field has been calculated self-consistently.•The ring can resonate at a set of frequencies corresponding to the excitation of different current eigenmodes in the ring.•The multiple-resonance behavior of a dielectric ring is completely neglected by the LCR circuit model.•The LCR circuit model describes quantitatively well the excitation of the fundamental mode in the rings with the ratio of the internal radius to external radius greater than 0.4.•For wider rings the LCR model overestimates the resonance frequency of the fundamental resonance and underestimates its strength and bandwidth.

Magnetic response of a planar dielectric ring to an axially applied time-harmonic magnetic field is analyzed. We find the self-consistent distribution of the polarization current in the ring and its magnetic moment. It is shown that the magnetic moment exhibits multiple resonances corresponding to the excitation of different eigenmodes in the ring. The properties of the fundamental eigenmode are used to analyze the performance and limitations of an equivalent LCR circuit model.