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ECE3025_Exam3_Solutions_F2005

# ECE3025_Exam3_Solutions_F2005 - Problem 1(20 points A(8...

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Unformatted text preview: Problem 1. (20 points) A. (8 points) Write Maxwell‘s equations in both derivative and integral form: Derivative Form Integral Form Gt§=o mﬁeédfzﬁE-ﬁxﬂs :0 A m j E: em? gaze—6.5m»; es. ads: #59?“ if = - a??? me am 5.. 933 .12 2 Sigma 3‘5 B. (8 points) Write the oper name for each of the following terms and give the correct units. E: EKECJ'IQJC #:ng InfEUS’YIY Unitsofﬁ Vim _ ELEm-faic bumMEMENT FIELD H a D: ﬂELTTQIC__FLuj Dewar): UnitsofD C(zm n [MAGNETIC meow/ﬂan FfELlD ﬂ w!) 2. B: MAG u E 7'1; jw X DENSITY Units of B (M EMAGoEﬂcI-WELD :NrEusn—y Unitsofﬁ AZ/m C. (2 points) Write the equation to calculate the net electric flux over a surface and give the proper units for electric flux. %6: FSEQ 44,5 (couL0m63) D. {2 points) Write the equation to calculate the net magnetic ﬂux over a surface and give the proper units for magnetic flux. ¢: 5 ”3.2: 15 (weaEZS) November 22, 2005 2 ECE 3025C Exam #3 Problem 2. (25 points) An inﬁnite line charge of 25 x 10'” coulombs per meter is located 0.5 meters from a dielectric material as Show below. This line charge lies along the z axis at x = 0, y = 0.5 in free space, and the relative permittivity of the dielectric is 4. Point l’ is located on the boundary of the dielectric at x = l, y = O, z = 0. Hint: use Coulomb’s law A for a line charge, i.e, E 3 _p_ % , as a starting point for this problem, where E is the vector from the point 2775 R (005,0) t0 (1,0,0). A. (8 pts) What are the values of E and l) at point P Line Charge on the free space side of the boundary? 3* (0-0-5) ‘1 Point P a: Q A A 1 m 1 (19.0) :. l . 2g 3 - R = 96 ’ 0 - 9 '3 ' Kl / H A o S A x E —. 22319.... t 1...?) . -" l .2; A. A A E. WD’Z 49.53] = 3,69% “”33 U/mn 100(Irlg) A ,3. l ‘4 A A. _ — _— o .. , b-e,t=,.. 3w“ [34¢ l 333’“ shame—”52 — (.9? x10 .3 Cod/m7. B. (8 pts) What are the values of ii} and 13 at point P on the dielectric side of the boundary? EIH‘MA :; Can't 1—» EXI : EXI- Diuoﬁ ,_ mt 2D DY! : DY'Z. (92¢, 60 58' 1 ‘téo an' Ex: :EXL _ E E33; " _..:§.l D.“ ’ Dan... ‘3; Lies EZCEULO"): —.q§§) M/"”‘ b qu)‘, XL —-lo A D: Libxﬁ’bgt : I-Z'huoqs —I.§‘i>< Nina C/M'z— November 22, 2005 3 ECE 3025C Exam #3 Problem 2. (Continued) C. (9 pts) Draw sketches of the voltage potential, E and B ﬁeld lines in the x-y plane. Hint: Plot the voltage potential and E on one plot, and B on a second plot. _/ @ M —> 5 oﬂpnﬂ’ L,:UET H a U 16 ﬁll/11:5 Dlﬁoﬁc’ﬂ 1 Tee “i FIELD LINES LIF. (£me ow “FOP m: THE E FIELD ewes TLHZU _.b E 1 60:;— .5 3 “Leo 5‘ QEéva a; 85—6/0“ @ November 22, 2005 4 ECE 3025C Exam #3 Problem 3. (25 points) Two concentric, cylindrical sheets of current have their centers located at the origin in the x—y plane, and both are inﬁnite in extent in the z direction. The inner cylinder has a radius of 5 mm and carries a current of 5 amps in the positive z direction. The outer cylinder has a radius of 10 mm and carries a current of 10 amps in the negative 2 direction. The material between the conductors has a relative permittivity of 2.5 and a relative permeability of 3.8. For all other regions the values for both the relative permittivity and permeability are 1. Express all answers in complete vector form, reduced to numerical answers, and give the proper units to receive full credit. A. _. £,=2.5.;1,=—“3.3 y A. (8 pts) Calculate the values of H and B for the region 5 mm < r < 10 mm deﬁned by r < 5 mm. £,=1,;rr=1 r<5mm,r>10mm r”: 30 mmwm‘t 1: 4“ 2 amps! __..J B. (8 pts) Calculate the values of E and 1—3 for the region deﬁned by 5 m < r < 10 mm. I?) —> '2‘ .8 ’1 3% "W‘0 99:35 .a=3 We >9 42- -43" B=~ Esme e /M?_ November 22, 2005 5 ECE 3025C Exam #3 1 1 umcul J. [Lonunueuj C. (9 pts) Calcuiate the values of E and E for the region deﬁned by r > 10 mm. BmWW A ' A S—IOA _ ”S CL H‘ﬁgeyw‘ 6 A“ B: _o."(CfGQ{U‘x157) g wig/m; IT. a; 'L’A «53-259 WW November 22, 2005 6 ECE 3025C Exam #3 Problem 4. (30 points) An inﬁnite conducting cylinder lies along the z axis at (x=0, F0) and carries a time varying current of 20 1(1) = T (23ﬂ + at) cos(120m) amps. This conductor has an inner diameter of 3 mm and an outer diameter of 5 5 mm, and the current is uniformly distributed over the volume of the conductor. The regions inside the conductor and outside the conductor are free space. Reduce your answers to numerical values with the proper vector components and units to receive full credit. Note that this conductor has both axial and circumferential current components. A. (4 pts) Does this current function represent a traveling wave in the z direction along this line? Circle: YES or STATE THE REASON FOR YOUR ANSWER. 20 1 6W1: W 6’2.- m(mt"(52) x in: “- '7: 3“. H. MS“ 9“)le B. (5 pts) Calculatizjthe'cdrigrit‘dconsilﬁsithin the conductor, i.e., the region deﬁned by 3 mm< r< 5 mm. WWW &9th£&i‘-W Jr? 1:? 2 Re milléfl‘fl vac/m; 5: T(.oos7‘—- - 0652‘) TL 008 «003) 3:; : lﬂ‘axtog mﬂllon't) 7:;an Ib- _ is. 2 it)“ milmr‘by f— “ -:. .__.———————-—-—" -* . .007. m“ Jé‘ GODS .. .0033cl> 007. Y'Sj J” ‘zcciLi'KU? MUwﬁ't) WM“?— ﬂow yitﬁmo a + m‘éxw ﬁgmomﬁyﬁi November 22, 2005 7 ECE 3025C Exam #3 Problem 4. (Continued) C. (7 pts) Calculate E for the region deﬁned by r ‘5 3 mm.‘ T0 VHF- IJ}, TEJZM 7"; l , §HJLQI H3d3+J+ S +y I O W A}, C. & O a” W OK‘ 05‘ ALLA: 2252.0 SOHEJQ : 30—941; = 0.00239, = 1:9. «003 67?- _,,_ H .—. :93: namowmg 1%; mam D. (7 pts) Caiculate 1—1 for the region deﬁned by r > 5 mm. .—-9 THE. cum” @mmreur‘zou wxu, BE Fey/v1 _L ‘. Do AclKQULAR (MTEéJZA'WDIU (.5013 Nd THE X’Y PLANE A—T €>0.00§) YIELDS E: Elk—g = "\$1 0140101143) 5“ A7/m awn. ’0 November 22, 2005 8 ECE 3025C Exam #3 Problem 4. (Continued) E. (7 pts) For this same inﬁnite conducting cylinder which carries a time varying current of 20 [(1) = — (22!a + a2 ) (205020711) amps, calculate the EMF induced in a 50 mm diameter inductive loop which J5 encircles this cylinder at z = 0 in the x-y plane. fHUS 1..“— 1L:- . 02."; EMF -.= _. 4-... g g B nobuﬂe— dICi '2' t 9:0 1}ch 3% :2 FLOR-t km; 1’: No‘?‘ A- Puma-7 mos, Tb: o.oZ§ EMF = —— SE awnoizfé :2.in FULS‘I‘ FIND H2 F012 ‘t‘H-E— 6255-on 0-oosccéow5‘ +g= S )2. o .005- 3;, act, he BEA-109.5. H A: je[o.ooS'-—nj =~. _II.§‘_'_L[0.OOS-)Lj W Summnrbaumé leg F02. ALL. Raézous 16‘ (7:51;) )Q. C 0.003 H? 7- fmoog-JL] Ie— (%>3o.003¢11.£0.00§ 00°01 O 3 IL>0.005- November 22, 2005 9 ECE 3025C Exam #3 Additional Work Space: (Identify the problem that you are providing the work for) Li E CONTINUED Mm 20.035 000m EvALQPrTﬁ S H 12.50.12.) ILzo 0.005 0-003 2 Sign c917.) + g Ia (0-005-“1bij 2, LWECO 003) Jr 51032 005) (o. 003); .- \l 5J9 (Lfoxlo )Cto QUE—Q cam Quart) {:tNALL‘i’ : W337M0101rt> VoH’S 0m, EMF '— 0&3? MQ’ZOTF—C) HV November 22, 2005 10 ECE 3025C Exam #3 ...
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