Analysis and Computation of Electric and Magnetic Field by K. J. Binns

By K. J. Binns

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If a set of images is proposed for each region of a field, their validity can be tested directly. If a set is proposed for one region only, it can be verified by consideration of surface charge distribution. A simpler check is possible when the boundaries are equipotential or flux line, for then the boundary conditions are easily seen to be satisfied by the system of images which is symmetrically disposed about all the boundary lines. (1) (2) (3) (4) (5) 37 38 ELECTRIC A N D MAGNETIC FIELD PROBLEMS It is convenient here to consider images under two headings: firstly those due to plane boundaries, and, secondly, those due to circular boundaries.

Therefore, substituting for (CDjAB) in eqn. 30) Also the position of the image is that of the inverse point of the position of the doublet with respect to the circle. The inclination of the doublet is seen, from a consideration of the similar triangles, as AB -*• 0, to be equal and opposite to that of the doublet (with respect to the line joining them). The image of a doublet inside the circular boundary can be found in a similar way to the above. Cylindrical boundary in applied uniform field. The influence of a circular boundary on a uniform applied field can be accounted for simply by using a doublet at infinity to give the uniform field and then by forming images, of this doublet, in the boundary.

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 . V. JAY AW ANT, Flux distribution in a permeable sheet with a hole near an edge, Proc. Instn. Elect. Engrs. 107 C, 238 (1960). 13. J. F. H . DOUGLAS, Reactance of end-connections, Trans. Am. Inst. Elect. Engrs. 5 6 , 2 5 7 (1937). 14. P. J. LAWRENSON, The magnetic field of the end-windings of turbo-generators, Proc.

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