  The effect of strong quantizing magnetic field on the nucleation of quark
matter droplets and on the chemical evolution of nascent quark phase at the
core of a neutron star are investigated. The surface energy of quark phase
diverges logarithmically. As a consequence there can not be a first order
transition to quark phase. However, a metal-insulator type of second order
transition is possible unless the field strength exceeds $10^{20}$G. The study
of chemical evolution of newborn quark phase shows that in $\beta$-equilibrium
the system becomes energetically unstable.
