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hw1_solution1

hw1_solution1 - So/u'l’ion ECE604 Homework 1 Out Tuesday...

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Unformatted text preview: So/u'l’ion ECE604 Homework 1 Out: Tuesday, January 11, 2005 Due: Tuesday, January 18, 2005 These problems are from Chapter 1 of the text by Ramo, Whinnery and Van Duzer (3rd edition, 1994). 1) 1.2f 2) 1.30 3) 1.4b 4) 1.4d 5) 1.7a 6) 1.8a 7) 1.8d + 8) 1.8h — 31mg _ 9) 1.9 5 an on Thursaltﬁ‘. l/g. 10)1.10d GQAMQQ—g) glen_rN_:g§l¢_ _C~J_Q 6145+ Jul—«.0 4a ngwrpdh :ﬂi—_ -. <55! :9 W0&&ichm «was "(—vq—a eva—a disk WNW. ”CM%_ \$414 Wﬁtli‘:_.%. S—‘hk%1~¥ ‘R’W P.9'VL+.__ _.__-..... 1e/msi'e {; ~~ Applloingv BWSS'S Law ”to calindrical surFace at arbitrané r'adius..i :11:re-ECH= enclosed charge =‘ ﬂytr’hur’dr' = 21:90., “ti: “ﬁg-g) Total beam current I. = rib-(r) 2.er l-4b .— ‘°’“d JGFJ’Vr ‘J’FCHSJEYJD +5.(%H at ) ' => 1» = 2.1m}? r0 ~s;(&)‘3[«+ axis—.Har = m.-(Ji #éh‘éaw r émraECr) 5m); (§*%‘g). ’ (~54?) 1» - _ 19L _ =E(r)lréa =W "5%) , C. 1t. ._._ 3 4 I -]:;('L~\$:. 0 0v ‘3‘ ; EQJLML " (4*1‘5"15*‘EG§5 'R’l'éu L514 § \w. 43m H—th-J am“ 41(35. FsFS+ §c\\I£—— “Q9" 9pm ﬂ¢c0a09 Q A ' ”WWI“? oww 4dr bo‘g‘m ,msled-wxé \$6) N420»! can/NE, '70”) @75‘1mﬂt‘1 awe 25 xmommo (Mama, -{—__\....~ X. 41.5 H For hid-.6}: LITv-z Ere LIP§C3 ‘ éEh= ”El: 4:0 Sfmb‘c . jQVWJDSUQ . . l‘ - \$9MM, 99‘9“?“ 4%.,on =3 mom ' . " = - M WWW“? ' - ; .- ?¢f‘ “7% ED : qwiq3/4Wrie : Sb 0.3\ j " . - Eel-F“ NV» Qxﬁs V. " W>I€ “\$9 , cad-wig)" K=co, FKJIUA lb MYAMS Mom. «,5qu 1% 47M; ahwgm-Axos Is 1‘ 'E)‘ :‘Qn'QX-JB 5 ”ﬁg-\JJ: Be- EK 2-2???an 53"“‘33 > ”“4"" +ng aw“. ' ("I m , (I A ’0M9°3*1ﬁ“"‘* Lf”-‘——.—' =4”?- ELA 134x) [X1 >1; . Ex . I’B'E [X1 Qc—d'); .-.3 d'bv‘X A‘GQA‘JD {g EX = E? E" . ._ 53 .. . ._ - -3. ' __.. . _ .. awe—1.x 2.6a: 51’36 [X C‘xld )1] 6-)" F. = X :x% +13)“ k F d£= =J.%de+jdg +1 zﬂdxieﬂ 0&3 . ' = 51+ \$I‘+ax‘\,gg+t-a+o=—§—+\ Fﬂ= L'Odg-t-f: zxdx +jL‘x‘amA-e’gz-‘ldl (Jimax4qa31 = 3.: at“ +3 ﬁgdxlgaz+r #JBIXMQ = 3;;xe +30 ax‘dx +3: 054 32;“... 3':+7’§"° :11. %_ .L,_:§. .1. ' Not conservative, since integrals are not zero ‘Por‘ arbibmrg, e. 05) \$239 93 - 159 - \$2.? at: n£ldx+3zfotdx+S2Ax+ﬂodx=l—l-2.=—2 E4 " §¢ = a. 4116.!" 0. =1;— = l—___—_—r 6. (52-45) + aw,— a LlOd‘ Emu) = é‘ewﬁ” —%ébn% were { ﬁtﬁﬁn, acréb 41;:er ’ b<r<c b gdr +_Ic gdr 4ft r2. = L(”‘ 5 5“ 5>= “3‘2"” w] €=—V§=e.x§_53 b 41:63“; '7: 4‘1? [2.(11. % #[c*+“+‘1{__s._.s_é>_.c_ms__gw‘~‘=>+w - _ w; 4x)“: [6‘ ~g)(:: 5’31 £=¢Lﬁ\$ﬁiw "+ ’1 - _ Simpwioaﬁon gives ‘ ' b ‘ I - _ E = £3 mi“ (“‘“é‘i-h‘l ﬁns} [MM-(gr? w r.= L(x+glzyt+3z]‘% . . \$3... .3; 1t ...
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