The electrical and physiological properties of ion channels are experimentally measured by inserting the channel into a lipid membrane separating two baths containing solutions of specific concentrations. A constant electrostatic bias is applied across the channel by immersing the electrodes in the two baths. Formulating boundary conditions that accurately represent these contact regions may require enormously large bath regions and is a challenging task. Beyond a Debye length from the membrane the electrostatic potential and ion densities do not vary appreciably. This assumption has been supported by the results of continuum results presented earlier. For typical salt concentrations used in ion channel simulations, the Debye length is of the order of 10 Å. Using the assumption, Dirichlet boundary conditions are imposed on the potential at the two domain boundary planes that are transverse to the channel, taking care that these planes are sufficiently far from the membrane.