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# Examples a potential between two semicircular plates

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Unformatted text preview: omplex plane) then E = F'(z) , where F(z) is the associated complex potential. Example Find the electric field corresponding to Example (D). 31 Notes 1. The Third Dimension In all of the above, we take the third coordinate to be the zcoordinate, which we cannot call z for obvious reasons! So, I suppose we can call it Ω , and write ∞(x, y, Ω) = The same formula for ∞ we used in the above examples since it is independent of Ω. 2. Haven't we done this before? Earlier, we solved Dirichlet's problem using conformal mappings, but had to first solve it on a simpler region —usually H. Here we are doing it again, from first principles, and interpreting it as electrostatic force. Also, it is good to do things several ways. Exercise Set 9 1. Find the potential, complex potential, equipotential lines, and lines of force of between two parallel plates at x = -5 and x = 10 having potentials 200 and 500 volts respectively. 2. Find the potential, complex potential, equipotential lines, and lines of force between two coaxial cylinders with radii 1 and 5...
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