  We consider quantum fluctuations of current in a metallic loop induced by
varying magnetic flux. The dependence of the fluctuations on the flux change
$\Phi$ contains a logarithmically divergent term periodic in $\Phi$ with the
period $\Phi_0=hc/e$. The fluctuation is smallest near $\Phi=n\Phi_0$. The
divergence is explained by a comparison with the orthogonality catastrophe
problem. The $\Phi_0-$periodicity is related with the discreteness of
"attempts" in the binomial statistics picture of charge fluctuations.
