Exactly solvable model for electromagnetic field in air of a three-phase power line over the Earth

Considerable effort has been focused on the investigation of ELF electromagnetic fields and their interaction with the human body. Much of this effort is concerned with the fields generated by high-voltage transmission lines at frequencies of 50 and 60 Hz. In order to calculate the induced currents in the body for its various orientations near a power line, it is desirable to determine accurately all vector components of the electromagnetic field in the air. There is a need to describe more accurately components which are parallel to the power line and, therefore, vanish in the absence of the Earth. The paper provides: (i) exact integrated formulas for all components of the field in the air, which are valid at any distance from the power line, and (ii) set of simplified expressions for cases of practical interest. Specifically, when the observation point falls into distances of a few meters away from the transmission line.