The fundamental principle behind a molecular electronics (MoleE) device is similar to that driving many resonant electron scattering or transmission processes; initial insertion of an electron into a resonance state, propagation in some manner (coherent, incoherent, or diffusive) that is a controllable characteristic of the resonance-supporting system, and final extraction of the selectively transmitted electron. The stages of a MoleE system responsible for the three-step conduction are often referred to as donor, bridge, and acceptor. The scattering or resonance properties depend amongst other things, upon the electrostatic potential profile along the bridge or molecular wire. Since the molecular wires are packed together within a self-assembled monolayer in real MoleE devices, the present study focuses on the electrostatics and dynamics of such structures, here formulated as a problem in cavity QED of a structured, polarizable continuum film of the bridge material inserted between parallel metallic plates rather than as one in conventional quantum chemistry. The plates (electrodes) and the molecular film are each characterized by their dielectric response functions and the donor/acceptor-electrode interactions by charge redistribution required to satisfy the appropriate electrodynamic boundary conditions. This approach provides fresh insights into the overall features of the electrostatic potential profile and select atomic-scale properties such as electrode-induced shifts in the resonance (aka HOMO and/or LUMO) energies within the molecules which in turn are crucial in determining the current-voltage characteristics of the MoleE device, as will be demonstrated.