  We investigate the impact of electrostatics on the proximity effect between a
magnetic insulator and a semiconductor wire in
semiconductor-superconductor-magnetic insulator hybrid structures. By
performing self-consistent Schr$\ddot{\rm o}$dinger-Poisson calculations using
an effective model of the hybrid system, we find that large effective Zeeman
fields consistent with the emergence of topological superconductivity emerge
within a large parameter window in wires with overlapping layers of magnetic
insulator and superconductor, but not in non-overlapping structures. We show
that this behavior is essentially the result of electrostatic effects
determining the amplitude of the low-energy wave functions near the
semiconductor-magnetic insulator interface.
