ps13 - A 2/z has a relation with the Milne-Thompson Circle...

This preview shows page 1. Sign up to view the full content.

MATH 406: Problem Set 13 due Wednesday, April 27, 2005 1. (a) Without using any facts about electromagnetism (except that the electrostatic potential is harmonic), guess the functional dependence of the potentional φ 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 C . (b) Using superposition, ﬁnd the total electric potential due to this charge in a spa- tially constant ﬁeld E 0 . 2. (a) Show that the Zhukovsky mapping w = z + (
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: A 2 /z ) has a relation with the Milne-Thompson Circle Theorem for a circle of radius R = A . (b) (based on Fisher 4.2.15) Show that the Zhukovsky map transforms ﬂow past a circle with R < A to ﬂow past an ellipse with axes a and b < a (see Fisher p.282). (c) Describe what happens when A → R . Why is this diﬀerent from your answer to part (a)? HINT: it is. 3. Find the Fourier transform ˆ u ( ω ) for the following functions of time t : a) u ( t ) = 5 1 + t 2 b) u ( t ) = 1 20 + 8 t + t 2 (F 5.1.5) Version 1.0...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online