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Note for ECE 2317 with Professor Jackson at UH Gauss law


Note for ECE 2317 with Professor Jackson at UH Gauss law

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This 9 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 26 views.

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Date Created: 02/06/15
Electromagnetics Workshop Solutions Electric Flux Problem 1 Given the eleCLI lC ux density D3 50057 A 717p quot 29p cosZ gt A CmZ Find the net electIic ux in the upward 2 direction through the annulus shown in the gure below agpgb X 1 forms ds2pdpd S 27 17 Zn 11J9pcosz pdpd 3b3 fag I cos2 d n w37rb37a3 C Electromagnetics Workshop Solutions Electric Flux Problem 2 A charge Q nC is at the origin of a spherical coordinate system Calculate the electric ux crossing the portion of a spherical shell described by 0 S 639 S g in the outward sense Solution 4727quot2 m2 D4m2QDr Q Total ux N a 6 1 g 27 D12 sin6d6d g g Q risinadadgj g sin d dg Electrom agnetics Workshop Solutions Gauss s Law Problem 1 Consider two long concentric circular cylindrical shells On the inner shell of radius 1 In there is a uniform surface charge density equal to 5 Cmz On the outer shell of radius 2 In there is a uniform surface charge density equal to 5 Cmz Find the electric field in all regions Electromagnetics Workshop Solutions Gauss s Law Problem 2 A point charge of strength q C is located at the center ofa spherical cloud of nonuniform charge density pV 2 7 ra Crng The radius of the spherical cloud is a Find the vector electric eld E at all points in space including the region inside the charge density and outside the charge density Z y X 1rle 04K af QM 3 ngrrwmeopde 5 000 Y a q I Y 393 9 3 LL o m 9 Ltd 77 T 0 2 l 1 129quot My 4quot Electromagnetics Workshop Solutions Gauss s Law Problem 3 An in nite planar slab of charge exists from x 0 m to x 2 m and has volume charge density pV x l Cm3 a Sketch the charge distribution as a function of x Label appropriate values on the vertical aXis b Find the electric eld in all regions State all assumptions and show all work I pv2x l Cm b CLAVge is add so no Evaisle slab d5 QuizL A A x Q 39on A gix l VDxgt gtlt a 39 D gtlt gtlt 3 E 0 15h xlt0 D e E 7 E gtlt2r1 x A X X J l 21 T K X y 0ltxlt2 60 E O 71 p2 Electromagnetics Workshop Solutions Gauss s Law Problem 4 A very long cylinder of uniform constant volume charge density pV K 4 Cm3 has a radius of p 4 n1 Surrounding this charge is a very long cylinder of uniform surface charge density p K8 Cmz having a radius of p 8 n1 K 4 and K 8 are arbitrary constants Find the electric field vector in all regions of space Gerun IIml Ilwe elcclrie eld vector in all three regions ofspuce j E 39 A S p lt 4 m gt mi zrl A 8l Z fw tgdwaigf fuypdefa quot 21L CI 000 ZWFL KI JiP1 26 L lt I gtEr quot 3491 pzb lml L lt Elt 8 EM mt bf K 201 5k M Eff L llltplt8 1 K4Cm pl p K3 1C 1 ml P gt 6 Eu 21rle Kl Jz39 t121rl1 11h gt2wpmpwllttznaslltszwh ffkef ll lf 00 8 at 8KquotK f 6 f 2978 M l Electromagnetics Workshop Solutions Gauss s Law Problem 6 An in nite slab of charge of volume charge density pVcoszsinz and thickness 7139 is centered about the zaXis as shown below Find the electric eld at all points in space this includes the regions both inside and outside the slab 0 szcoszsinz For the cosine varying charge Z 7r2 HDZiid14 DZi idA2DZAA J cosz dz Atomquot fir2 7r2 lso zZIr2 2D s1n 2 3 E Z 2 Z lso zS Ir2 HDZiid14 Dzi 2DZA AT cosz dz Amp Aboutquot Z2sinz 3 EZSmZ Sz Z so 2 2 2DZ sinz For the sine varying charge J39J39DZiidA Dzi idA2DZAAHj sinzdz0 Amp Atom 42 EZ0 lleIr2 jjpzi2dADzAAT sinz dz Amp fir2 DZ coszZ2 cos 3 Z cosz Sz 4 go i 221 so 2 Using superposition E2 i z S so 2 sinz cosz ltZlt g 2 2 Electromagnetics Workshop Solutions Gauss s Law Problem 7 A line source of constant charge density pi0 that exists along the zaXis is surrounded by an electrically neutral metal cylinder of thickness b a and a cylinder with uniform charge density pV0 ofthickness d c Note that d gt c gt b gt a a Find the electric eld in all regions b What must the value of pV0 be so that the electric eld is zero for p gt d c Now that the metal cylinder is grounded Modify the answers in part a to obtain the electric eld in all regions pm Solution pie2 forplta Q foraltpltb a 21 pmg forbltpltc Vm l39goJ p0pvoirp2 cz forcltpltd p0pvo dZ CZ forpgtd pro 3 b va az Cm pie2 forplta Q foraltpltb 0 21 9 forbltpltc Vm gop pv0 p2 Cz forcltpltd pv0 d2 Cz forpgtd Electromagnetics Workshop Solutions Gauss s Law Problem 8 a Given an electric ux density vectorl yzi3yx2xzz Cm2 l nd the value of the total charge Q contained within the cube with one vertex at 000 and the diagonally opposite vertex at 111 The point coordinates are measured in meters b What is the value of the net electric ux out of the cube c A point charge q C is added at 1000 Now what is the value for the net electric ux out of the cube d The point charge in c is moved to 121212 Now what is the value for the net electric ux out of the cube Solution 11 11 3 1 a QmQ dSI3xdxdzx2dxdy C S 00 00 2 3 6 11 b wz C 11 c wz C 11 l 7 d VIEE C


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