Open AccessInduction in a Non‐Uniform Conducting Half‐Space by an External Line Current
Author(s) -
Weaver J. T.,
Thornson D. J.
Publication year - 1972
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1972.tb06120.x
Subject(s) - conductor , earth's magnetic field , current (fluid) , electromagnetic induction , perturbation (astronomy) , electrical conductor , boundary value problem , physics , plane (geometry) , geometry , mathematical analysis , magnetic field , line (geometry) , mathematics , quantum mechanics , electromagnetic coil , thermodynamics
Summary A two‐dimensional problem in electromagnetic induction which is of interest in explaining the effect of a coastline on geomagnetic variations is solved analytically. The model considered consists of a periodic line current above a non‐uniform earth, represented by a conducting half space with a horizontal plane boundary and divided by a vertical plane into two regions of different conductivities. The solution for the field is generated by perturbation from the corresponding solution for a perfectly conducting earth. Limiting expressions for the field are derived for the case when the height and magnitude of the line current approach infinity in such a way that the inducing field near the Earth becomes uniform and finite. The variation of the field at the surface of the conductor is shown for a line current at finite height and the variations at different heights above the conductor are shown for a uniform inducing field. The latter results are compared with those recently obtained by numerical methods.