  We study the fractionalization of an electron tunneling into a strongly
interacting electronic one-dimensional ring. As a complement to transport
measurements in quantum wires connected to leads, we propose non-invasive
measures involving the magnetic field profile around the ring to probe this
fractionalization. In particular, we show that the magnetic-field squared
produced by the electron and the power that it would induce in a detector
exhibit anisotropic profiles that depend on the degree of fractionalization. We
contrast true fractionalization with two other scenarios which could mimic it
-- quantum superposition and classical probabilistic electron insertion. We
show that the proposed field-dependent measures and those of the persistent
current can distinguish between these three scenarios.
