  The dynamics contained in magnetized layers of exoplanet atmospheres are
important to understand in order to characterize what observational signatures
they may provide for future observations. It is important to develop a
framework to begin studying and learning the physical processes possible under
those conditions and what, if any, features contained in them may be observed
in future observation missions. The aims of this study is to formally derive,
from scaling arguments, a manageable reduced set of equations for analysis,
i.e. a magnetic formulation of the equations of quasigeostrophy appropriate for
a multi-layer atmosphere. The main goal is to provide a simpler theoretical
platform to explore the dynamics possible within confined magnetized layers of
exoplanet atmospheres. We primarily use scaling arguments to derive the reduced
equations of "magnetoquasigeostrophy" which assumes dynamics to take place in
an atmospheric layer which is vertically thin compared to its horizontal
scales. The derived equation set retains features existing in standard
shallow-water magnetohydrodynamic equations but are absent in more classical
derivations of the quasi-geostrophic limit, namely, the non-divergence of the
in-plane components of the magnetic field. We liken this non-divergence of the
in-plane magnetic fields as indicative of a quantity whose behaviour mimics a
two-dimensional "pseudo"-magnetic monopole source. We also find, using the same
scaling argument procedures, appropriate limits of the fundamental parameters
of the system which yield reduced equations describing the flow dynamics
primarily characterized by magnetostrophic balance. The standard scaling
arguments employed here show how traditional magnetized quasigeostrophic
equations connect to their magnetized shallow water forms. The equations
derived are amenable to analysis using well-known techniques.
