  Understanding the relationship between the magnetic field and coronal heating
is one of the central problems of solar physics. However, studies of the
magnetic properties of impulsively heated loops have been rare. We present
results from a study of 34 evolving coronal loops observed in the Fe XVIII line
component of AIA/SDO 94 A filter images from three active regions with
different magnetic conditions. We show that the peak intensity per unit
cross-section of the loops depends on their individual magnetic and geometric
properties. The intensity scales proportionally to the average field strength
along the loop ($B_{avg}$) and inversely with the loop length ($L$) for a
combined dependence of $(B_{avg}/L)^{0.52\pm0.13}$. These loop properties are
inferred from magnetic extrapolations of the photospheric HMI/SDO line-of-sight
and vector magnetic field in three approximations: potential and two Non Linear
Force-Free (NLFF) methods. Through hydrodynamic modeling (EBTEL model) we show
that this behavior is compatible with impulsively heated loops with a
volumetric heating rate that scales as $\epsilon_H\sim
B_{avg}^{0.3\pm0.2}/L^{0.2\pm^{0.2}_{0.1}}$.

Solar and Stellar Astrophysics