Solved Assignment 7 for Electromagnetism | PHYS 323, Assignments of Electromagnetism and Electromagnetic Fields Theory

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• 323 Homework set 7, Spring

323 Homework set 7, Spring 2007 Problem 10.19 =Aa-# Rood @ EF" ef Fit — (w/e)*sin® a]? The horizontal components cancel; the vertical com- v ponent of Rt is sin @ (see diagram). Here d = Rsin#, so J _ sin’? 2 = -d(~ csc? o) da = —1 ap, a Ie Re find cot é, so dz = —d( coc! 8) dé = rg tei — : 1 dsin?@ wei eS z di = Thus A y ™ sin8 . E = 20-0) ————__——_—_.. d@._ Let z =cos8, so sin? @ = 1-2”. 0-73) omg : _ A= w/c) ¥ 1 ~ dmeod -1 [L—(w/e)? “ores” _ AMb=v*fe*) GF] 1 - Anegd (v/e) (c2 fu? — WEF —1+z7} IL, -y Melee T= eR VFS = mie (same as for a line charge at rest). (b) B= lw x E) for each segment dg = Adz. Since v is constant, it comes outside the integral, and the same formula holds for the total field: 1 24 Ho 2Au 11 B= 5x8) = jv Pre x 9) = Mev dae ad But Av = J, s0|B= wot @| (the same as we got in magnetostatics, Eq. 5.36 and Ex. 5.7).