  Analytical models of axially symmetric thin disks of finite extension in
presence of magnetic field are presented based on the well-known Morgan-Morgan
solutions. The source of the magnetic field is cons\-tructed separating the
equation corresponding to the Ampere's law of electrodynamics in spheroidal
oblate coordinates. This produces two asso\-ciated Legendre equations of first
order for the magnetic potential and hence that can be expressed as a series of
associated Legendre functions of the same order. The discontinuity of its
normal derivate across the disk allows us to interpret the source of the
magnetic field as a ringlike current distribution extended on all the plane of
the disk. We also study the circular speed curves or rotation curve for
equatorial circular orbits of charged test particles both inside and outside
the disk. The stability of the orbits is analyzed for radial perturbation using
a extension of the Rayleigh criterion.
