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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.
1. Repeat 1 of the non-hand in work for plates along y = 2 - x and y = 4 - x with
voltages as above.
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
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
a complex (analytic) potential function F: HÆC . Precomposing this with another
analytic map D...
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