  We present scaling laws for advection, radiation, magnetic drag and ohmic
dissipation in the atmospheres of hot giant exoplanets. In the limit of weak
thermal ionization, ohmic dissipation increases with the planetary equilibrium
temperature (T_eq >~ 1000 K) faster than the insolation power does, eventually
reaching values >~ 1% of the insolation power, which may be sufficient to
inflate the radii of hot Jupiters. At higher T_eq values still, magnetic drag
rapidly brakes the atmospheric winds, which reduces the associated ohmic
dissipation power. For example, for a planetary field strength B=10G, the
fiducial scaling laws indicate that ohmic dissipation exceeds 1% of the
insolation power over the equilibrium temperature range T_eq ~ 1300-2000 K,
with a peak contribution at T_eq ~ 1600 K. Evidence for magnetically dragged
winds at the planetary thermal photosphere could emerge in the form of reduced
longitudinal offsets for the dayside infrared hotspot. This suggests the
possibility of an anticorrelation between the amount of hotspot offset and the
degree of radius inflation, linking the atmospheric and interior properties of
hot giant exoplanets in an observationally testable way. While providing a
useful framework to explore the magnetic scenario, the scaling laws also reveal
strong parameter dependencies, in particular with respect to the unknown
planetary magnetic field strength.
