Note on air-gap and interpolar induction
Journal of the Institution of Electrical Engineers
The publication of Messrs. Hawkins and Wightman's recent dissertation on the "Air-gap Induction in Continuous Current Dynamos" 1 induces me to present to the Institution the following note on the subject of the fringe of lines near the edge of a pole-piece. It need hardly be pointed out in this place that the exact solution of the magnetic problem presented by a dynamo is impossible without an almost inconceivable addition to our present mathematical knowledge. Hence we are driven to making
... riven to making various assumptions about the shape of the lines of force in order to obtain a more or less approximate estimate of the strength of the field at the armature surface. Such assumptions often lead to sufficiently accurate results over limited regions, but are liable to break down where a solution is most wanted. Thus it is practically correct to assume that the lines of force pass straight across the air-gap, and that they form arcs of circles outside the air-gap-so long as we are not near the edge of the pole-piece, but the solution fails in the immediate neighbourhood of that edge. Messrs. Hawkins and Wightman's process of rounding the corner of the curve at discretion 2 can hardly be regarded as satisfactory. In the following I propose to give the exact solution of some comparatively simple, though ideal, problems concerning the field of force near the edge of a pole-piece, in order to provide a criterion whereby to judge of the merits of the various approximate formulae used in this connection, to indicate the order of accuracy that may be expected from the use of these formulas, and to furnish a plausible means of correcting the results which they lead to. The first problem to be discussed is the two-dimensional one of the lines of force from the pole-piece to the armature shown in Fig. i , when the pole-piece is supposed to be at one magnetic potential, and the armature at another.