  Optically levitated macroscopic objects are a powerful tool in the field of
force sensing, owing to high sensitivity, absolute force calibration,
environmental isolation and the advanced degree of control over their dynamics
that have been achieved. However, limitations arise from the spurious forces
caused by electrical polarization effects that, even for nominally neutral
objects, affect the force sensing because of the interaction of dipole moments
with gradients of external electric fields. In this paper we introduce a new
technique to model and eliminate dipole moment interactions limiting the
performance of sensors employing levitated objects. This process leads to the
first noise-limited measurement with a sensitivity of $3.3\times10^{-5}e$. As a
demonstration, this is applied to the search for unknown charges of a magnitude
much below that of an electron or for exceedingly small unbalances between
electron and proton charges. The absence of remaining systematic biases,
enables true discovery experiments, with sensitivities that are expected to
improve as the system noise is brought down to or beyond the quantum limit. As
a by-product of the technique, the electromagnetic properties of the levitated
objects can also be measured on an individual basis.
