Generalizing a previous result by two of the authors (MSA and AAA) for an infinite sheet with one insertion, we derive two coupled linear Fredholm integral equations of the second kind on two coplanar contours for the determination of the magnetic field due to an infinite plane electrical conducting sheet with two non-overlapping insertions, permeated by a uniform, parallel electric field. These equations are solved numerically to provide solutions for new problems involving two elliptic insertions. The level lines for the current function in the sheet are plotted and the results are discussed to assess the efficiency of the numerical method. The conclusions are relevant to non-destructive testing of electrical conducting sheets and to the evaluation of magnetic fields on the earth’s surface around islands. Generalization to any finite number of insertions is straightforward.
M. El-Sakout, D.; F. Ghaleb, A.; S. Abou-Dina, M.; and A. Ashour, A.
"The Magnetic Field of Electrical Conducting Sheets with Two Non-Overlapping Insertions,"
Applied Mathematics & Information Sciences: Vol. 09:
3, Article 14.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss3/14