EE 311 Exam 3_solutions - Name Section: (check one)...

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Unformatted text preview: Name Section: (check one) Chappell Jiao April 23, 2009 ECE 311 Exam 3 Spring 2009 Closed Text and Notes 1) Be sure you have 17 pages. 2) Write only on the question sheets. Show all your work. If you need more room for a particular problem, use the reverse side of the same page. 3) No calculators. 4) Write neatly. If your writing is illegible, then print. 5) The last 6 pages contain equations that may be of use to you. Feel free to separate these pages from the rest of the exam booklet. 6) This exam is worth 100 points. (Signature) Problem ABET Outcome Points I Score —._l 1 1o ‘ ‘ 2 10 3 10 fl—————. 4 5 *_—“ 5 iv 10 6 V 10 7 V _ _— -— —_ —_— 3 (10 pts) 1. A current of 1 A is flowing in a loop shown below. ‘ 0 = 2 m ' (a) If the loop is placed in a uniform magnetic field of 1—5” = 10051} T, what is the maximum torque received by the loop? y l = 1 A V 4 I WWW ,ng M”; l + x 7” :r: m Ki“ t? +——-—-————-—> b = 1 m a WE —» (b) If the loop is subject to a vector magnetic potential of A = x52 , in which plane the loop rests after it has rotated? w y I f got 7 -L{J€w,/ :6, v f ' a g "A ‘2‘ x“ ('7 f n “NAM “M37 M) [61:] a; I, ‘‘‘‘‘ v Q \ 4 (10 pts) 2. A 1 C charge of mass 2 kg is moving in a uniform magnetic field E = 1031z T. The velocity of the charge is known to be 2? = 2 ><105 5x m/s at time t: 0. What is the kinetic energy of the charge at t= 4 s? 1’ m i mi» ; [ff/V? i5 (W s 2* V :3 *5 € 2. K / a: g f «~\ f! {1,}! j! MA f, {f f ' «e- ~ i "“ t w 2r"; 5 (10 pts) 3. A solid dielectric sphere of relative permeability 4 is placed in free space. The radius of the sphere is l m. The H field is known to be H = 251’]. + 453 A/m inside the sphere. No current flows on the surface of the dielectric sphere. The H field outside of the sphere is A) H = 0.52;, i m B) F1 = 0.521,. + 250 141 m A a a A C) H=0.5ar +406 +4a¢— m C) H = 43g 5 m K». R .7 f D) = 852, + 4% i g" H EM" Roof m a, , a. a. VJ 5? w z” .A E)H=2&r+2ag£ {’1’ H” be H 2 m .55.; 9‘; r . F) None of the above 1! H ‘2' )1 A Whit“ k . L (é / k ‘ (L If. :3: [ZN/arr. (5 pts) 4. a] E 0 d1 = 5 V, which one ofthe following is true? A) TE 0 (11 is independent of the path y A (:B) is due to time—varying sources. C) E is due to static charges. D) <1 E 0 dl cannot be nonzero. E) None of the above. 6 (10 pts) 5. Derive the inductance per unit length for two parallel plates partially filled with a material having relative permeability of 100. The cross-sectional View of the structure is shown in the (xx/~13 following figure. The length direction (current flowing direction) is into the paper. kaiser; i? g) (:1 ks}; cgfimrxii éiF‘SE/“r‘éém / 4‘74“ "i" ":5" //~/;,’ 5) V W V, jam"; i 7 (10 pts) 6. Shown is a circuit consisting of two resistors. A magnetic field exists inside the circuit loop. The magnetic flux out of the page is known to be l// = (101 + 5) Wb . What is the reading V on the voltmeter shown? 8 (lSpts) 7. The sliding rod in the following figure is located on two rails that are separated by 1m. At time t = 0, the rod is atx = 1 m. After 1‘ = 0, the rod is pulled in the +x direction as shown at velocity of 1 m/s. In the shaded region from x = 2 m to x = 4 m, there exists a magnetic flux density of 10672 T . Plot the current versus time in the 10 £2 resistor from 1‘: 0 to t= 6 s. The reference direction of the current i is given in the figure below. 9 (30 pts) 8. The region of space for z < 0 is filled with a dielectric of relative permittivity 4; the region for z > 0 is free space. The electric field for z < 0 is given by E = (26—jflz " ejflz)ax V/m. The frequency of the wave is 1 GHz. (5 pts) The velocity of the wave in z < 0 region is m . A) 3x108 — f S (if? i. “WM W W“ f; m ,2’ £5 if B)f1.5 x108 — a n ("V C) 6 x 10 8 — S D) None of the above (5 pts) The wavelength of the wave in z < 0 region is A) m N ting” B)j:0.15 m ' a] C) 0.2 m L??? D) 0.3 m E) None of the above (5 pts) The wave number (propagation constant) of the wave in z < 0 region is mm” rad/s 3 I“; f «wka 3 rad / s ism!” 3 D) None of the above 10 (5 pts) In region 2 < 0, wave is propagating in A) y direction B) —y direction C) 2 direction D) —z direction E) x diection F) ~x direction ,a- v wng G) None of the above (5 pts) In region 2 > 0 which is free space, E field has x—component only MNB) y—component only C) z—component only D) x— and y— components E) x- and z-cornponents F) y- and z—cornponents G) None of the above (5 pts) Derive the instantaneous form of H for z < 0 region ...
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This note was uploaded on 02/12/2012 for the course ECE 311 taught by Professor Peroulis during the Fall '08 term at Purdue University-West Lafayette.

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EE 311 Exam 3_solutions - Name Section: (check one)...

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