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Slowly varying electromagnetic fields play a key role in various applications in bio-systems and medical engineering. Examples are the electric activity of neurons on neurochips used as biosensors, the stimulating electric fields of implanted electrodes used for deep brain stimulation in patients with Morbus Parkinson and the stimulation of the auditory nerves in deaf patients, respectively. In order to simulate the neuronal activity on a chip it is necessary to couple Maxwell's and Hodgkin-Huxley's equations. First numerical results for a neuron coupling to a single electrode are presented. They show a promising qualitative agreement with the experimentally recorded signals. Further, simulations are presented on electrodes for deep brain stimulation in animal experiments where the question of electrode ageing and energy deposition in the surrounding tissue are of major interest. As a last example, electric simulations for a simple cochlea model are presented comparing the field in the skull bones for different electrode types and stimulations in different positions.