  A theoretical model is developed to study the equilibrium electromagnetic
properties of a spherically symmetric dust molecular cloud (DMC) structure on
the Jeans scale. It applies a technique based on the modified Lane-Emden
equation (m-LEE). It considers an inhomogeneous distribution of dust grains in
field-free hydrodynamic equilibrium configuration within the framework of exact
gravito-electrostatic pressure balancing condition. Although weak relative to
the massive grains, but finite, the efficacious inertial roles of the thermal
species (electrons and ions) are included. A full portrayal of the lowest-order
cloud surface boundary (CSB) and associated parameter signatures on the Jeans
scale is made numerically for the first time. The multi-order extremization of
the m-LEE solutions specifies the CSB at a radial point m relative to the
centre. It gets biased negatively due to the interplay of plasma-boundary wall
interaction (global) and plasma sheath-sheath coupling (local) processes. The
CSB acts as an interfacial transition layer coupling the bounded and unbounded
scale-dynamics. The geometrical patterns of the bi-scale plasma coupling are
elaborately analyzed. Application of the proposed technique to neutron stars,
other observed DMCs and double layers is stressed together with possible future
expansion.
