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To investigate Casimir electromagnetic interaction in $N$ bodies, weimplement multiple $\delta$-function plates with electric and magneticproperties. We use their optical properties to study the Casimir energy betweenthe plates by implementing multiple scattering formalism. We initially solveGreen's functions for two and three plates configurations to obtain theirreflection coefficients. Further, the coefficients are implemented in multiplescattering formalism, and a simple method was obtained to depict energy densitydistribution 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 andnext-to-nearest neighbour scattering terms represented by different loopsdepending on reflection, transmission and propagation distance. In this manner,the Casimir energy density was generalized to $N$ plates by identifying asystematic pattern in the representation of diagrammatic loops.

Casimir energy of $N$ magnetodielectric $\delta$-function plates