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The Quarterly Journal of Mechanics and Applied Mathematics 1950 3(4):420-434; doi:10.1093/qjmam/3.4.420
© 1950 by Oxford University Press
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NOTE ON DIFFRACTION BY AN EDGE

D. S. JONES

( Dept. of Mathematics, The University Manchester )

On the assumption that the electric current and charge on a perfectly conducting sheet are integrable in the neighbourhood of the edge, it is shown that the line distributions of electric current and charge on the edge are determined by the boundary conditions on the sheet. As a boundary condition on the edge it is postulated that there be no line distributions of magnetic current and charge; it is shown that the field is then determined uniquely. It is also proved that, if the currents near the edge can be expanded in power series, the index of the first term is (2p+1)/2, where p is an integer, greater than –2 or –1 according as the current parallel or perpendicular to the edge is considered. Finally the diffraction, in three dimensions, of a plane wave by a semi-infinite plane is obtained.


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