By K. J. Binns
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Additional info for Analysis and Computation of Electric and Magnetic Field Problems
For both of these, consideration is given to the field of line charges (or currents), but the effect of a single circular boundary on an applied uniform field (images of doublets) is also discussed. 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.
For a line charge q per unit length in an electric field of strength E, the force is Eq\ for a line pole in a magnetic field it is Hm \ and for a line c u r r e n t in a magnetic field it is Bi. 2. 3). The field strength at the position of an element is calculated as that due to all the field influences except the source considered. If the field of the other elements of the source is taken into account, the force calculated includes a contribution from the internal forces in the source and these sum to zero when the total external force is calculated.
The images which can be used to give the field inside the region are shown in Fig. 6(a), (b), and (c) for the values n = 2,3 and 4. ) For all values of n, the image currents lie on a circle, its centre at the point of intersection of the boundaries and passing through the current, i. The currents in the complete system (the images and the actual currents) are alternately positive and negative and are symmetrically disposed about the boundaries. Consequently, this system gives rise to flux lines along the boundaries, so confirming the validity of the solution.
Analysis and Computation of Electric and Magnetic Field Problems by K. J. Binns