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MIT6_013S09_exam

MIT6_013S09_exam - 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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6.013 Electromagnetics and Applications Student Name: Final Exam Closed book, no calculators 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 ( π , ε o , μ o , η 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. MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 1 Problem 1. (25/200 points) Two square capacitor plates in air have +Q d o 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 = ε - Q b b Please turn sheet over to answer parts (b) and (c). - 1 - 5/16/09

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b) A perfectly conducting plate is introduced d/10 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? d σ = +Q - Q L ε o x y z b C b = 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.
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MIT6_013S09_exam - 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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