Induced Voltage in an Open Wire

Abstract

Abstract A puzzle arising from Faraday’s law has been considered and solved concerning the question which voltage will be induced in an open wire with a time-varying homogeneous magnetic field. In contrast to closed wires where the voltage is determined by the time variance of the magnetic field and the enclosed area, in an open wire we have to integrate the electric field along the wire. It is found that the longitudinal electric field with respect to the wave vector contributes with 1/3 and the transverse field with 2/3 to the induced voltage. In order to find the electric fields the sources of the magnetic fields are necessary to know. The representation of a spatially homogeneous and time-varying magnetic field implies unavoidably a certain symmetry point or symmetry line which depend on the geometry of the source. As a consequence the induced voltage of an open wire is found to be the area covered with respect to this symmetry line or point perpendicular to the magnetic field. This in turn allows to find the symmetry points of a magnetic field source by measuring the voltage of an open wire placed with different angles in the magnetic field. We present exactly solvable models of the Maxwell equations for a symmetry point and for a symmetry line, respectively. The results are applicable to open circuit problems like corrosion and for astrophysical applications.