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Unformatted text preview: ÆH therefore gives us a complex potential DÆC , and hence a harmonic
function ∞:DÆI . This is exactly what we were doing two sections ago, and now we do
it some more, this time in the context of complex potentials.
(A) Potential between two semicircular plates
Consider the following scenario: 32 3 kV insulation
We would like a conformal mapping sending the disk to H . Without being too
demanding, let us go back to Example (B) on p. 23 of these notes, where we saw that
takes the above disc onto the right-hand half-plane as shown:
3 kV –3 kV –3 kV So what we need now is a nice potential for the right-hand region. But this is an angular
one, so our potential is given by (see the last section)
∞ = Aø + B
= πArg(z) (Recall that Arg is fine for the right-hand plane; -π < Arg(z) ≤ π)
This is the imaginary part of πLn(z) or the real part of -iπLn(z). Thus ∞ is the real part of
F(z) = -iπLn(z)
Transferring this over the left-h...
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