MATH 406: Problem Set 13
due Wednesday, April 27, 2005
- 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
- Using superposition, find the total electric potential due to this charge in a spatially constant field
- Show that the Zhukovsky mapping
has a relation with the Milne-Thompson Circle Theorem for a circle of radius
- (based on Fisher 4.2.15) Show that the Zhukovsky map transforms flow past a circle with
to flow past an ellipse with axes
(see Fisher p.282).
- Describe what happens when
. Why is this different from your answer to part (a)? HINT: it is.
- Find the Fourier transform
for the following functions of time