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Non-diagonal elements of impedance matrix expressing mutual impedance between x-th and y-th conductor can be written as: hat{Z}_{x,y} = l_{v} R_{g} + R_{E} + {text{j}}4uppi l_{v} f times 10^{ - 4} ln left( {frac{{D_{g} }}{{d_{x,y} }}} right) (19 where d x,y is distance between x-th and y-th conductor.
end{gathered} (17) In terms of the magnetic scalar potential these boundary conditions correspond to a non-zero magnetic flux (phi_{i}) through any ray originating from the i-th conductor and a zero magnetic flux through any ray originating from any other conductor.
If the i-th conductor has a non-zero electric potential (phi_{i}) and all the others are grounded, the boundary conditions at the interface are given by begin{gathered} phi x,0) = phi_{i}, quad a_{i}< x< b_{i}, phi x,0) = 0, quad a_{j}< x< b_{j}, j neq i, frac{partialphi}{partial y} x,0) = 0, quad a_{j}< x< b_{j+1}.
These points must exist since (a_{j}) and (b_{j}) lie on the j-th and (j+1 -th conductors respectively, both of which are grounded, so the integral of the electric field along any contour connecting them must be equal to zero.
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