  The intricate interplay between complex permittivity and permeability
constitutes the cornerstone of electromagnetic (EM) applications, enabling
precise customization for various uses. This study employed silver-epoxy
nano-composites to exemplify a conductor-insulator composite, leveraging
silver's exceptional attributes, such as high conductivity and low reactivity.
The determination of complex permittivity and permeability was conducted via
the transmission/reflection method. At lower concentrations of dispersed silver
particles, these nano-particles within the epoxy resin act as modest dipoles,
augmenting permittivity. This regime aligns closely with the effective medium
theory (EMT) and comprises the focus of much research. However, nearing the
percolation threshold, a percolation effect emerges, drastically accelerating
enhancement rates beyond the predictions of EMT. Simultaneously,
long-wavelength electromagnetic waves induce diamagnetic currents within loops
formed by metal grains. This diamagnetic effect intensifies with increasing
volume fraction, leading to a reduction in permeability. This study observed
percolation power law behavior near the threshold with calculated critical
exponents. Consequently, the dielectric constant of the silver-epoxy
nano-composite reached a maximum of 515. Regarding permeability, the lowest
recorded value was 0.31. These findings were obtained within the X-band (8.2
GHz~12.4 GHz) region.
