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Additional resources for Analysis and Computation of Electric and Magnetic Field Problems

Sample text

J. LAWRENSON, The magnetic field of the end-windings of turbo-generators, Proc. Instn. Elect. Engrs. 108 A , 538 (1961). Additional Reference MACK, C , The field due to an infinite dielectric cylinder between two parallel conducting plates, Br. J. Appl. Phys. 6 , 59 (1955). 1. Introduction The method of images, because of its simplicity, is of considerable value, but for many problems involving multiple boundaries or specified distributions of potential or potential gradient, it is more convenient to solve the field equations directly.

Because of the limitation in the values of the angles of intersection, only one combination of four boundaries is possible, namely, that with all the interior angles equal to nj2. The positions of the images of a line current for the field with flux-line boundaries are shown in Fig. 7. The distribution of the images is doubly periodic, and they are symmetrical about each of the boundary lines, so that, as required, these are flux lines. Letting the field be in the /-plane, the origin and dimensions being as shown in Fig.

Consequently, this system gives rise to flux lines along the boundaries, so confirming the validity of the solution. 9 (a) (b) FIG. 6 It can be shown that in general the number of images is (2«~1), and that the angles subtended by the images at the intersection of the boundaries form the series where 6 is the angular displacement of the current from one of the boundary lines. When the boundaries are infinitely permeable, the images are in the same positions as the above, but they all have the same sign as the actual current.