ECE3025_Exam3_Solutions - ECE 3025D -- Electromagnetics...

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Unformatted text preview: ECE 3025D -- Electromagnetics EXAM #3 April 19, 2005 ~ Page 1 of 7 Name: K E Y 1 Student Number: 1. Check that your exam includes all 7 pages (cover, 4 problems). 2. Read all instructions and problems carefully. Points will be deducted for failure to follow instructions. 3. Please print your name and student number at the top of this page, and print your name at the top of all the subsequent pages. 4. Show ALL of your work to receive full credit, and put the proper units on all numerical problems. 5. Do all your work on the page of the problem, and if necessary on the back of the preceding page. 6. You are permitted one sheet (8 1/2 x 11, double-sided) of handwritten notes. Use of any other notes, books, or other resources is prohibited. You are to turn in this sheet with your exam. 7. Calculators are permitted; however, you are not allowed to use the calculator memory to store notes, etc. 8. No cell phones are permitted during the exam. 9. This exam lasts for 75 minutes. Point values are listed for each problem to assist you in best using your time. 10. The Georgia Tech honor code applies. To recognize the implications, please sign the following: "I did not give or receive aid during this exam, nor will I discuss the exam with anyone who intends to take it at a different time" Signature: Problem 1. (25 points possible) Problem 2. (25 points possible) Problem 3. (25 points possible) Problem 4. (25 points possible) TOTAL. (100 points possible) 1 .9 .7 l 8 Some useful values: 80 =——-——- x10 (F/m), #0 =47! x10 (H/m), co = = 3 X 10 (W8) 36” \H‘ogo KEY Problem 1. (25 points) Name: A. (10 pts) Sketch the electric field and voltage potential lin for a electric dipole co of opposite sign separated by a distance . April 18, 2005 2 nksxng of two point charges ECE 3025D Exam #3 E Name: Problem 1. (Continued) C. (10 pts) Sketch the magnetic field lines for the line of current shown below. Assume that this current loop lies totally in the (x, y) plane. April 18, 2005 3 ECE 3025D Exam #3 NmzKEY Problem 2. (25 points) A boundary, at x = 0 , separates two regions in space with different electrical permittivities and magnetic permeabilities. For region 1, the half space defined by x < 0 , ,u = yo and 6‘ = 80. For region 2, the half space defined by x > 0 , ,u = 4.5 #0 and 8 = 2080 . The fields at x = 0— are E = 25 )2 + 5 y-S 2(V/m)and H] = 5 § -20§I+5 2(A/m). Findthefields E2, H2, 52, and E2 in . + . . . . reglon 2 at x = 0 . Express answers IS complete vector form w1th reduced numerical answers and proper units. .— _q a O ,L: ELEZ = Z—g-QWXlO (I.ZS)S)—-S)( 441) EL ; 2.2 7’2 + 33.92% — 8.823,) x 10””(C4Aa) M: H: El: “7312, ’— Ho (Li.§><\ ' \l )’20) S) (w'o/ML) Eu“- WWLO’WWSD (Wr'w, 9') (“w/ma) Ef-(bm 9’: —H3.( ’3‘ + 73.3} x (0' % April 18, 2005 4 ECE 3025D Exam #3 KEY Problem 3. (25 points) Two concentric conducting cylinders are aligned along the z axis. The inner cylinder has Name: a radius of a = 5 cm, and the outer cylinder a radius of b = 20 cm. The total current carried by the inner cylinder is I A = 10 2 amps, and the total current carried by the outer cylinder is IB = - 20 z. The region between the cylinders is filled with a material of relative magnetic permeability ,u, = 7.5 , and for all other regions ,ur = 1. Express answers is complete vector form with reduced numerical answers and proper units. A. (4 pts) Calculate the current density on the inner cylinder) AWHA—Q, WCQM—Qaast Hzo Bzo «64m JL<0~9011 hzo-ga. C. (7 pts) What are the components and values of H and E for r = 0.5 (a + b)? )1: oong§§ = chgc/m = 0.95% 3111‘ MM: 80 H631 &e z among: Mme) Hg \0 > ’ ‘|ZSC2)TF: lZ.73 A/Ma—‘z H @144 : p0 L13) um's oz. - 5) E :— {.2 x to QCW‘DAK”) . (7 pts) Wh tare the components and values of H and B for r = 2. fl: QngZO)”§OCVV\-' OoS/yy) A “o g oz H - Rrr(o~'5) April 18, 2005 5 ECE 3025D Exam #3 KEY Problem 4. (25 points) For the region in space defined by z < 0 , a 10 KHz plane wave propagates in the Name: positive 1 direction in a source free region of free space; i.e., a lossless medium with ,u = [10, 8 = so, 0' = 0 . For 2 < 0 the electric field is given by _F:(z,t) = E0 cos(a)t — flz) x where fl = a) #080 . The region in =1, 0' = 3.2 x107(S/m). space defined by z > 0 is a good conductor with constitutive parameters 8, = ,u, A. (10 pts) Write the equation for the electric field, E(z, t ) , for z > 0. Put in specific values for all the wave ’ 303$) = E0 mat—(béfi 6, xx 0“; (3’1"- WW‘ = troo“>(awx:57)<3.zxt073 3 (5 W :: an”; = 6.237“; ml ) Etgifi: El, 6? A -IIZO (9)0 étgtt) : on amiavgmé‘t—memgfl 3 (W33 B. (8 pts) Write the equation for the magnetic field, fi(z,t), for z > 0. Put in specific values for all the wave ' “Mt—E“: 71mm M2 terms to receive full credit. dot /‘ (t— D -ow,‘ w F136 30 Name: K Y Problem 4. (Continued) C. (7 pts) What is the 2 value for which the electric field is attenuated 20 dB from its value at z = 0+ ? 30A?) ::> ‘i‘lo a 0.1 April 18, 2005 7 ECE 3025D Exam #3 ...
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This note was uploaded on 01/27/2011 for the course ECE 3025 taught by Professor Citrin during the Spring '08 term at Georgia Institute of Technology.

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ECE3025_Exam3_Solutions - ECE 3025D -- Electromagnetics...

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