  We study the effects of a large-scale, ordered magnetic field in
protoplanetary disks on Type I planet migration using a combination of
numerical simulations in 2D and 3D and a linear perturbation analysis.
Steady-state models of such disks require the inclusion of magnetic
diffusivity. To make progress using ideal MHD, we focus on simplified field
configurations, involving purely vertical ($B_z$) and azimuthal ($B_\varphi$)
field components and a combination of the two. For each of the models we
calculate the locations of the relevant resonances and of the turning points,
which delineate the propagation regions of the MHD waves that transport angular
momentum from the planet to the disk. We use both numerical and semianalytic
methods to evaluate the cumulative back torque acting on the planet, and
explore the effect of spatial gradients in the disk's physical variables on the
results. We conclude that, under realistic (3D) circumstances, a large-scale
magnetic field can slow down the inward migration that characterizes the
underlying unmagnetized disk --- by up to a factor of $\sim 2$ when the
magnetic pressure approaches the thermal pressure --- but it cannot reverse it.
A previous inference that a pure-$B_\phi$ field whose amplitude decreases fast
enough with radius leads to outward migration applies only in 2D. In fact, we
find that, in 3D, a pure-$B_\phi$ disk undergoes a rapid transition to
turbulence on account of a magnetorotational instability that is triggered by
the planet-induced appearance of a weak $B_z$ component.
