  The magnitude of the inverse Faraday effect (IFE), a static magnetization due
to an ac electric field, can be strongly increased in a mesoscopic sample,
sensitive to time-reversal symmetry (TRS) breaking. Random rectification of ac
voltages leads to a magnetization flux, which can be detected by an asymmetry
of Hall resistances in a multi-terminal setup. In the absence of applied
magnetic field through a chaotic quantum dot the IFE scale, quadratic in
voltage, is found as an analytic function of the ac frequency, screening, and
coupling to the contacts and floating probes, and numerically it does not show
any effect of spin-orbit interaction. Our results qualitatively agree with a
recent experiment on TRS-breaking in a six-terminal Hall cross.
