In this article, the self-inductance of a circular circuit is treated from an untraditional, particle-based point of view. The electromagnetic fields of Faraday induction are calculated explicitly from the point-charge fields derived from the Darwin Lagrangian for particles confined to move in a circular orbit. For a one-particle circuit (or for N non-interacting particles), the induced electromagnetic fields depend upon the mass and charge of the current carriers while energy is transferred to the kinetic energy of the particle (or particles). However, for an interacting multiparticle circuit, the mutual electromagnetic interactions between particles can dominate the behavior so that the mass and charge of the individual particles becomes irrelevant; the induced fields are then comparable to the inducing fields and energy goes into magnetic energy. In addition to providing a deeper understanding of self-inductance, the example suggests that the claims involving hidden mechanical momentum in connection with momentum balance for interacting multiparticle systems are unlikely to be accurate.