Multiple magnetic field sensors are arranged around a current-containing volume at multiple longitudinal and circumferential positions. Each sensor measures multiple magnetic field components and is characterized by one or more calibration parameters. A longitudinal primary current flows through two end-to-end electrical conductors that are separated by an arc gap, and flows as at least one longitudinal primary electric arc that spans the arc gap and that moves transversely within the arc gap. Estimated transverse position of the primary electric arc is calculated, based on the longitudinal position of the arc gap, and two or more of the measured magnetic field components along with one or more corresponding sensor positions or calibration parameters. In addition, estimated occurrence, position, and magnitude of a transverse secondary current (i.e., a side arc) can be calculated based on those quantities.