15_5_17 - 17 The surface Since is given by x = e u cos v y...

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Unformatted text preview: 17. The surface Since is given by x = e u cos v, y = eu sin v, z = u, for 0 u 1, 0 v . (y, z) eu sin v eu cos v = = -eu cos v 1 0 (u, v) (z, x) 1 0 = u = -eu sin v u e cos v -e sin v (u, v) (x, y) eu cos v -eu sin v = u = e2u e sin v eu cos v (u, v) the area element on dS = is e2u cos2 v + e2u sin2 v + e4u du dv = eu 1 + e2u du dv. is 1 + e2u , then the total charge is 1 If the charge density on S 1+ e2u dS = 0 e (1 + e ) du e3u 3 1 0 u 2u dv 0 = eu + = (3e + e3 - 4). 3 ...
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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