- 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 and (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
:
a) b) (F 5.1.5)

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