  Magnetoelectric effect of the spin-1/2 Heisenberg-Ising ladder in a presence
of the external electric and magnetic fields is rigorously examined by taking
into account Katsura-Nagaosa-Balatsky mechanism. It is shown that the applied
electric field may control a quantum phase transition between the N\'eel
(stripy) ordered phase and the disordered paramagnetic phase. The staggered
magnetization vanishes according to a power law with the Ising-type critical
exponent 1/8, the electric polarization exhibits a weak singularity and the
dielectric susceptibility shows a logarithmic divergence at this particular
quantum phase transition. The external electric field may alternatively invoke
a discontinuous phase transition accompanied with abrupt jumps of the
dielectric polarization and susceptibility on assumption that the external
magnetic field becomes nonzero.
