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GRATICULES FOR THE COMPLETE DETERMINATION OF THE MAGNETIC FIELD OF HOMOGENEOUSLY MAGNETIZED CYLINDRICAL BODIES WITH ARBITRARY CROSS SECTION AND FINITE LATERAL EXTENSION *
Author(s) -
HELBIG KLAUS
Publication year - 1964
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1964.tb01895.x
Subject(s) - symmetry (geometry) , cross section (physics) , cylinder , computation , plane (geometry) , point (geometry) , physics , extension (predicate logic) , field (mathematics) , section (typography) , geometry , magnetic field , plane symmetry , mathematical analysis , classical mechanics , mathematics , computer science , quantum mechanics , algorithm , pure mathematics , programming language , operating system
Graticules are known for the calculation of the magnetic field of homogeneously magnetized “two‐dimensional” structures. For bodies whose lateral dimensions are comparable with the dimensions of the cross section and/or the distance between the point of observation and the structure, these graticules allow an approximative computation of the field in the plane of symmetry only. The degree of approximation can be improved by means of end corrections, but the amount of work involved increases rapidly. Moreover, even with end corrections the applicability of the graticules is still restricted to cases of rather simple geometry. In this paper, a set of graticules is proposed which already incorporates all end corrections. The set consists of three graticules, and it can be shown that at any point of observation lying outside the body each graticule needs be applied once only in order to calculate any component of the magnetic field produced by a homogeneously magnetized cylinder of arbitrary cross section, finite lateral extension and arbitrary spatial orientation. Curves and tables have been prepared, which allow the construction of the graticules under consideration. The application is illustrated by a hypothetical example. Possibilities for further improvements of the method are discussed.