The thermal noise threshold at biological membranes for electromagnetic field (EMF) effects is considered. Increased EMF sensitivity occurs when cells are connected by gap junctions (short circuits) in a tissue structure. A distributed parameter electrical model represents this cell array structure and shows the transmembrane voltage to thermal noise ratio increases by a maximum factor of 103 as array length progresses from 10 μm (single cell) to a physiologically relevant length of 1 mm. Maximal spatial amplification occurs at much lower frequencies than for the corresponding single cell. This places the EMF sensitivity of the target well within the frequency range of environmental sources, and provides new guidelines for improved therapeutic signals.