Since these rays extend from 0 to infinity they must

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Unformatted text preview: cm with inner cylinder charged to 10 volts and the outer cylinder charged to 100 volts. 3. Find the associated electric fields in each of these cases. Hand In 1. Repeat 1 of the non-hand in work for plates along y = 2 - x and y = 4 - x with voltages as above. -1 2. Show that F(z) = sin z may be regarded as the complex potential associated with the two horizontal lines (-Ï, -1] charged with one potential and [1, Ï) charged with another. Sketch some equipotential lines and lines of force. Hence find the associated electric field. 3. Verify the claim that A [ Arg (z-c) - A rg (z+c)] = Const are circles. [Hint: Express Arg(z-c) + Arg(z+c)] in terms of the angle between z-c and z+c] 10. Using Conformal Maps to Find Electric Potentials and Fields: Based on Kreyszig's Excellent Book We know that harmonic functions are the real (or imaginary) part of an analytic function. Therefore, if ∞ is harmonic on the upper half-plane; ∞: HÆI , then ∞ is the real part of R a complex (analytic) potential function F: HÆC . Precomposing this with another I analytic map D...
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