By K. J. Binns
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Extra info for Analysis and Computation of Electric and Magnetic Field Problems
4. Images are also very useful for solving three-dimensional fields, involving plane boundaries with any shape of conductor, for example, in problems involving windings near iron boundaries/ » but a discussion of these does not fall within the scope of the book. 2. Plane boundaries The images for a line charge near an infinite plane boundary are first established, and then the results for this boundary are extended to give solutions for various combinations of plane boundaries. These include two parallel and up to four intersecting plane boundaries, the angles of intersection being submultiples of^r.
17) In the air region, r can become infinite, but, as the potential at infinity must be finite (equipotential lines stretch from infinity to the current and (dip/dr) = 0) all values of c must be zero. 18) In the iron, r can be zero so that, as the potential at the origin must be finite, d must be zero. This region does not contain a current or pole, so there are no additional terms. 19) and it remains to determine d and c from the continuity of the two functions ip and xpj on the cylinder surface.
L . BAYLEY, Some applications of the method of images, Phys. Rev. 17,147-56 (1921). 8. G . B . WALKER, Electric field of a single grid radio valve, Proc. Instn. Elect. , Part III, 98,57 (1951). 9. S. FRANKEL, Characteristic impedance of parallel wires in rectangular troughs, Proc. Inst. Rad. Engs. 182 (1942). 10. D. c. machines), Electrotechnicky Obzor 4 4 (8), 395 (1955). 11. J. H . GRIDLEY, The shielding of overhead lines against lightning, Proc. Instn. Elect. Engrs. 107 A , 325 (1960). 12. B .
Analysis and Computation of Electric and Magnetic Field Problems by K. J. Binns