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categoryرياضيات schoolبكالوريوس event_available2026-07-14

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3. The Neumann integral for ellipses. 6.1. Find the Neumann integral (no need to solve it) for the case of two concentric ellipses with semi-major axis A and a and semi-minor axis B and b, respectively. Assume the two ellipses belong to two parallel planes at a distance 6 from each other, as shown in Fig. 3.3. [15 points] 6.2. Show that the result found in 6.1 reduces to the Neumann integral for a circle when A B and a b. Consider then the solution Eq. (4.8) of Eq. (4.7) in page 105 of the notes. Assume A a 1 m and 6e-1/4r with r = 1 mm. Under these conditions, & can be assumed to be small. Using these numerical values and following closely all derivations in the notes, compare the approximate result for M21 when considering the first two terms (i.e., up to 2) in the series expansions (4.11a) and (4.11b) for F(k) and E(k) in page 106 of the notes to the approximate result obtained when considering just the first term in the series expansions (4.12a) and (4.12b) in the notes, i.e., In 4/k, and 1. [10 points] A B 이 Figure 3.3

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