MATH 406: Problem Set 13

due Wednesday, April 27, 2005

1. Without using any facts about electromagnetism (except that the electrostatic potential is harmonic), guess the functional dependence of the potentional for a purely radial electric field, which is due to an isolated electric charge (such as an electron). Define your reasoning clearly, and specify the associated analytic function in .
2. Using superposition, find the total electric potential due to this charge in a spatially constant field .

1. Show that the Zhukovsky mapping has a relation with the Milne-Thompson Circle Theorem for a circle of radius .
2. (based on Fisher 4.2.15) Show that the Zhukovsky map transforms flow past a circle with to flow past an ellipse with axes and (see Fisher p.282).
3. Describe what happens when . Why is this different from your answer to part (a)? HINT: it is.

1. Find the Fourier transform for the following functions of time :

a)    b)    (F 5.1.5)

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