  We examine the spatial distribution of electric charges within an extended,
non-conductive cylinder featuring an inner radius denoted as $r_{0}$. Our
investigation unveils the emergence of a distinct modified attractive-inverse
square potential, arising from the intricate interplay between the electric
field and the induced electric dipole moment of a neutral particle. This
modified potential notably departs from the conventional inverse-square
potential, showcasing an additional term proportional to $r^{-1}$. As a result,
we present compelling evidence for the realization of a discrete energy
spectrum within this intricate system.
