  We study the phase separation configurations and their rotational properties
for a mixture of two interacting charged Bose-Einstein condensates subject to a
magnetic field trapped in disc and Corbino geometries. We calculate the ground
state energies of azimuthal and radial phase separation configurations using
the Gross-Pitaevskii and the Thomas-Fermi approximations. We show that the
results for experimentally relevant system parameters from both approaches are
in good agreement. The immiscible mixture in both geometries with equal
intracomponent interactions favors the azimuthal phase separation for all
intercomponent interactions. Only an imbalance in the intracomponent
interactions can result in a transition to the radial phase separation, for
which the transition becomes sensitive to the shape of the trap. We present
phase diagrams as a function of the inter and intracomponent interactions.
While the radial phase separation is widely favoured in disc geometry, the
azimuthal phase separation is favoured for narrower Corbino geometries. We
explore the rotational properties of the spatially separated condensates under
the magnetic field, studying their angular momenta and velocity fields. The
quantization of circulation breaks down for the azimuthal phase separation. In
this case, the bulk region of the condensate continues to display superfluid
flow behavior whereas the velocity field shows a rigid body behavior along the
phase boundaries.
