In this article, a closed-form expression for the impedance of a tangential eddy-current coil
in the presence of an infinite conducting wedge of arbitrary angle is derived. The truncated
eigenfunction expansion (TREE) solution given here is valid in the quasi-static frequency
regime. The theory was validated via comparison to an independent analytical expression
for the impedance change of a horizontal coil over a conducting half-space due to Burke.
We present results for three geometries: a conducting quarter-space, a conducting wedge of
angle 225 degrees, and a semi-infinite conducting sheet. Our theory predicts a measurable
change in the tangent coil reactance in the presence of all three geometries.
1. L. B. Felsen and N. Marcuvitz. Radiation and Scattering of Waves. IEEE Press, Piscataway, New Jersey
202 C. P. TRAMPEL AND J. R. BOWLER
2. J. R. Wait. Electromagnetic Radiation from Cylindrical Structures. Peter Peregrinus Ltd., London, UK
3. B. A. Mishustin. Radiophysics and Quantum Electronics 34: 82–85 (1991).
4. C. T. Tai. Dyadic Green’s Functions in Electromagnetic Theory. IEEE Press, Piscataway, New Jersey,
2nd Edition (1994).
5. T. P. Theodoulidis. Journal of Applied Physics 93: 3071–3078 (2003).
6. H. Sun, J. R. Bowler, and T. P. Theodoulidis. IEEE Transactions on Magnetics 41: No. 9, 2455–2461
7. Y. Li, G. Y. Tian, and A. Simm. NDT & E International 41: Issue 9, 477–483 (2008).
8. T. P. Theodoulidis and J. R. Bowler. Proceedings of the Royal Society of London: Series A 461:
No. 2062, 3123–3129 (2005).
9. E. J. Rothwell and M. J. Cloud. Electromagnetics. CRC Press LLC, Boca Raton, FL (2001).
10. J. A. Stratton. Electromagnetic Theory. McGraw-Hill, New York (1941).
11. A. Gray and G. B. Mathews. A Treatise on Bessel Functions and Their Applications to Physics.
Macmillan and Co., London, 2nd Edition (1922).
12. G.W. Hanson and A. B. Yakovlev. Operator Theory for Electromagnetics. Springer, New York (2002).
13. P. Henrici. Applied and Computational Complex Analysis: Vol. I. Wiley, New York (1988).
14. K. Yasumoto. Electromagnetic Theory and Applications for Photonic Crystals. CRC Press LLC, Boca
Raton, FL (2006).
15. I. S. Gradshteyn and I. M. Ryzhik. Table of Integrals, Series, and Products. Academic Press, London,
7th Edition (2007).
16. S.K. Burke. Journal of Physics D: Applied Physics 19: 1159–1173 (1986).