Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T10:17:38.619Z Has data issue: false hasContentIssue false
  • English
  • Français

Early quasi-steady electro-magnetic fields about conducting surfaces

Published online by Cambridge University Press:  17 February 2009

Graham J. Weir
Graham J. Weir
Affiliation:
Applied Mathematics Group, The New Zealand Institute for Industrial Research and Development, P O Box 31-310, Lower Hutt, New Zealand.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Step changes in current through either grounded or ungrounded wires lying on the surface of a uniformly conducting half-space produce image current sources within the surface the conductor. This image current is effectively the only source term for initial changes in ∂1Bz, Ex and Ey. The general steady state electric and magnetic field components resulting from steady currents flowing through either grounded or ungrounded wires of finite length lying on the surface of a uniform half- space are derived. Then the operators mapping these steady fields into the early values of ∂tBz, Ex and Ey on or above the conducting half-plane resulting from instantaneously stopping the current flow through the wires are derived.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 4 , April 2001 , pp. 481 - 493
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Abramowitz, M. and Stegun, I. A. (eds.), Handbook of mathematical functions (Dover, U.S. Government Printing Office, Washington, DC, 1965).Google Scholar
[2]Baños, A., Dipole radiation in the presence of a conducting half-space (Pergamon Press, Oxford, 1966).Google Scholar
[3]Corson, D. and Lorrain, P., Introduction to electromagnetic fields and waves (W. H. Freeman, San Francisco, 1962).Google Scholar
[4]Lee, T., “The effect of displacement currents on time domain electromagnetic fields”, Bull. Aust. Soc. Explor. Geophys. 12 (1981) 34–36.CrossRefGoogle Scholar
[5]Lewis, T. J. and Lee, T. J., “The detection of induced polarization with a transient electromagnetic system”, IEEE Trans. Geosci. Remote Sensing 22 (1984) 69–80.CrossRefGoogle Scholar
[6]Roberts, G. E. and Kaufman, H., Table of Laplace transforms (W. B. Saunders, Philadelphia, 1966).Google Scholar
[7]Sommerfeld, J. A., Electromagnetic theory (McGraw-Hill, New York, 1949).Google Scholar
[8]Stratton, J. A., Electromagnetic theory (McGraw-Hill, New York, 1941).Google Scholar
[9]Wait, J. R., “The magnetic dipole over a horizontally stratified earth”, Can. J. Phys. 29 (1951) 577–592.CrossRefGoogle Scholar
[10]Wait, J. R., “Propagation of electromagnetic pulses in a homogeneous conducting earth”, Appl. Sci. Res. B 8 (1960) 213–253.CrossRefGoogle Scholar
[11]Wait, J. R., Geo-electromagnetism (Academic Press, New York, 1982).Google Scholar
[12]Weir, G. J., “Singular spin harmonics”, J. Math. Phys. 20 (1979) 1648–1649.CrossRefGoogle Scholar
[13]Weir, G. J., “Transient electromagnetic fields about an infinitesimally long grounded horizontal electric dipole on the surface of a uniform half-space”, Geophys. J. R. Astr. Soc. 61 (1980) 41–56.CrossRefGoogle Scholar
[14]Weir, G. J., “Electromagnetic multipole propagation in a homogeneous conducting whole space”, J. Math. Phys. 23 (1982) 748–752.CrossRefGoogle Scholar
[15]Weir, G. J., “Forerunners on conducting surfaces: the infinitesimal vertical magnetic dipole with displacement terms”, Geophys. J. R. Astr. Soc. 81 (1985) 19–31.CrossRefGoogle Scholar