  To investigate Casimir electromagnetic interaction in $N$ bodies, we
implement multiple $\delta$-function plates with electric and magnetic
properties. We use their optical properties to study the Casimir energy between
the plates by implementing multiple scattering formalism. We initially solve
Green's functions for two and three plates configurations to obtain their
reflection coefficients. Further, the coefficients are implemented in multiple
scattering formalism, and a simple method was obtained to depict energy density
distribution in the multiple scattering expansions using diagrammatic loops.
The Casimir energy for $N$ bodies depends on multiple scattering parameter
$\Delta$; this parameter was distributed into nearest neighbour scattering and
next-to-nearest neighbour scattering terms represented by different loops
depending on reflection, transmission and propagation distance. In this manner,
the Casimir energy density was generalized to $N$ plates by identifying a
systematic pattern in the representation of diagrammatic loops.
