Some analytic solutions to Maxwell's electromagnetic equations for determining characteristics of eddy current probe coil configurations were derived years ago by Caius V. Dodd and co-workers. Links to some of their published solutions are listed below:
http://www.ornl.gov/info/reports/1969/3445602867360.pdf
http://www.osti.gov/bridge/servlets/purl/4155082-fjJn9k/4155082.pdf
Researchers at Riga Technical University have been developing solutions to Maxwell's electromagnetic equations with applications to various eddy current testing issues. A list of some of their publications is listed below:
http://www.wseas.us/e-library/conferences/2011/Cambridge/NEHIPISIC/NEHIPISIC-12.pdf
http://www.emc.rtu.lv/issue_46.pdf/antimirov_dzenite.pdf
http://www.wseas.us/e-library/conferences/2011/Meloneras/ACELAE/ACELAE-45.pdf
http://www.wseas.us/e-library/conferences/2009/rodos/SYSTEMS/SYSTEMS79.pdf