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7/13/09 - 1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.013 Electromagnetics and Applications Student Name: Final Exam Closed book, no calculators May 18, 2009 Please note the two pages of formulas provided at the back; the laser and acoustic expressions have been revised slightly. There are 10 problems; some are on the back sides of the sheets. For full credit, please simplify all expressions , present numerical answers to the extent practical without a calculator or tedious computation, and place your final answers within the boxes provided . You may leave natural constants and trigonometric functions in symbolic form ( , o , o , o , h, e, sin(0.9), 2 , etc.). To receive partial credit, provide all related work on the same sheet of paper and give brief explanations of your answer. Spare sheets are at the back. Problem 1. (25/200 points) Two square capacitor plates in air have separation d, sides of length b, and charge ±Q as illustrated. Fringing fields can be neglected. a) What is the capacitance C a of this device? C a = o A/d = o b 2 /d b) A perfectly conducting plate is introduced between the capacitor plates, leaving parallel gaps of width d/10 above and below itself. What now is the device capacitance C b when it is fully inserted? C b = C a ’/2 = o b 2 /2(d/10) = 5 o b 2 /d c) What is the magnitude and direction of the force f on the new plate of Part (b) as a function of the insertion distance L. Please express your answer as a function of the parameters given in the figure. C = o [5bL/d + b(b – L)/d] f = - dW T /dL = - dW T /dC dC/dL = - (Q 2 /2C 2 ) dC/dL = (Q 2 /2[ o b/d] 2 [b + 4L] 2 )4 o b/d = 2Q 2 d/ o b(b + 4L) 2 1 2 3 4 5 6 7 8 9 10____ ε o - Q d +Q b b C a = o b 2 /d C b = 5 o b 2 /d f = 2Q 2 d/ o b(b + 4L) 2
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7/13/09 - 2 - Problem 2. (20/200 points) The plate separation of a lossless parallel-plate TEM line many wavelengths long
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This note was uploaded on 02/02/2012 for the course EE 013 taught by Professor Staelin during the Spring '09 term at MIT.

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