  A magnetoelectric effect according to Katsura-Nagaosa-Balatsky mechanism in
spin-1/2 $XY$ chain in transverse magnetic field is considered. A spatial
orientation of the electric field is chosen to provide an exact solution of the
model in terms of free spinless fermions. The simplest model of quantum spin
chain demonstrating a magnetoelectric effect, a zero temperature case of the
spin-1/2 $XX$ chain in a transverse magnetic field with
Katsura-Nagaosa-Balatsky mechanism, is considered. The model has the simplest
possible form of the magnetization, polarization and susceptibility functions,
depending on electric and magnetic fields in a most simple form. For the case
of arbitrary $XY$ anisotropy, a non-monotonous dependence of magnetization on
the $XY$ anisotropy parameter is figured out. This non-uniform behaviour is
governed by the critical point which is connected with the possibility to drive
the system gapless or gapped by the electric field. Singularities of the
magnetoelectric susceptibility at the critical value of system parameters are
shown.
