Calculating the voltages induced in technological systems during a geomagnetic disturbance

During geomagnetic disturbances voltages are induced in electrically conducting networks such as power systems, pipelines, and phone cables. The voltage produced in a horizontal loop at the Earth's surface can be calculated by considering the changing vertical magnetic field through the loop or by calculating the electric field around the loop from the horizontal magnetic field variations. The two approaches are equivalent, both being a consequence of Maxwell's equations, however, this equivalence is difficult to visualize. By considering the nondivergent nature of the magnetic field, it is shown how the vertical magnetic field through a horizontal loop is related to the horizontal magnetic field at the periphery of the loop. The case of a magnetic disturbance due to a line current above the earth's surface is used to illustrate the equivalence of the two approaches for calculating the voltage induced in a conducting network.