Open AccessSome Results on the Magnetic Field of Electric Currents Induced in a Thin Hemispherical Shell of Finite Conductivity, with Geomagnetic Applications
Author(s) -
Doss S. S.,
Ashour A. A.
Publication year - 1971
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.1971.tb03608.x
Subject(s) - earth's magnetic field , electromagnetic induction , electric field , shell (structure) , magnetic field , rotational symmetry , scalar (mathematics) , physics , conductivity , field (mathematics) , scalar potential , electrical resistivity and conductivity , electromagnetic field , computational physics , geophysics , mechanics , geometry , classical mechanics , materials science , mathematics , quantum mechanics , electromagnetic coil , composite material , pure mathematics
Summary We consider the induction of electric currents in a thin uniformly conducting hemispherical shell by axisymmetric time‐varying fields. A method of successive approximation to the solution is developed; the first approximation corresponds to the perfectly conducting shell. Using the vector potential of the fields, the first and second approximations are obtained for certain external fields. The results for the first approximation agree with those obtained by Ashour using the scalar potential. However, the analysis given here is simpler. The results are applied to electromagnetic induction in a large ocean and to the effect of the concentration of the induced currents near the edge. For variations of periods up to 24 h, the second approximation is found adequate. The calculations made for a varying field of 24 h period show that the vertical component of the induced field is enhanced near the coastline in both sea and land, and is reversed in direction on crossing the coast. The horizontal (tangential) component of the field is enhanced near the edge in the sea.