Unformatted text preview: omplex plane)
E = F'(z) ,
where F(z) is the associated complex potential.
Find the electric field corresponding to Example (D).
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 ,
∞(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
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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