By K. J. Binns
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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. 3. Total force acting on a boundary Simple expressions for the total force acting on a boundary are derived in terms of the magnetic field; analogous relations exist for the electric field.
BASIC FIELD THEORY 29 stant so that the value of either cp or ip gives directly a quantity of flux or a value of potential difference. Note that cp and ip can be interchanged in eqn. 91) when convenient. 2) that cp and ip can be derived from each other, and it is now evident that, being conjugate functions, they are related by the Cauchy-Riemann equations. 93) These are based on the expression of the field in cartesian coordinates, but they may be expressed equally in the forms appropriate to other coordinate systems.
16) Use of all three of these equations is necessary only in the potential function for the region containing the pole. In all other regions the effect of the pole can be attributed to boundary magnetization and so included in the general series expression. Before considering some examples it should be noted that in employing the method of separation of the variables it is simplest to use separate potential functions for each region of a field, these functions being connected by the boundary conditions between the regions.
Analysis and Computation of Electric and Magnetic Field Problems by K. J. Binns