Open AccessE‐polarization induction in two thin half‐sheets
Author(s) -
Dawson T. W.
Publication year - 1983
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.1983.tb03808.x
Subject(s) - electromagnetic induction , polarization (electrochemistry) , magnetic field , singularity , half space , physics , conductor , discontinuity (linguistics) , condensed matter physics , geometry , mathematical analysis , mathematics , electromagnetic coil , quantum mechanics , chemistry
Summary. An analytical solution is obtained for the E‐polarization problem of electromagnetic induction in two adjacent half‐sheets underlain by a uniform conducting half‐space. In this mode the inducing magnetic field is assumed horizontal, uniform and perpendicular to the discontinuity. The same model was previously solved under B‐polarization by Dawson & Weaver. The present solution then completes the study of two‐dimensional induction in the described model. Further, it extends both the analytic E‐polarization solution of Weidelt by the inclusion of an underlying conductor and that of Raval, Weaver & Dawson by the inclusion of arbitrary conductance values for the two surface sheets. The solution may be used as an idealized model of the coast effect and allows detailed study of the field behaviour near the discontinuity. The horizontal magnetic field on each side of the surface layer has a finite jump discontinuity at the interface and the vertical magnetic field exhibits a logarithmic singularity there. If the right‐hand conductance (say) becomes infinite, the horizontal magnetic field exhibits an algebraic singularity as the coastline is approached from the right, while the vertical magnetic field does likewise from the left. Calculations are presented for the same two models as discussed in B‐polarization by Dawson & Weaver and the results are compared to values obtained from a more general numerical scheme. The electric current distribution inside the conducting half‐space is depicted for the second model.