  The scaling theory of Grossmann and Lohse (J. Fluid Mech. 407, 27 (2000)) for
the turbulent heat and momentum transfer is extended to the magnetoconvection
case in the presence of a (strong) vertical magnetic field. The comparison with
existing laboratory experiments and direct numerical simulations in the
quasistatic limit allows to restrict the parameter space to very low Prandtl
and magnetic Prandtl numbers and thus to reduce the number of unknown
parameters in the model. Also included is the Chandrasekhar limit for which the
outer magnetic induction field B is large enough such that convective motion is
suppressed and heat is transported by diffusion. Our theory identifies four
distinct regimes of magnetoconvection which are distinguished by the strength
of the outer magnetic field and the level of turbulence in the flow,
respectively.
