final_exam_2006

final_exam_2006 - School of Electrical and Computer...

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Unformatted text preview: School of Electrical and Computer Engineering, Cornell University 1 ECE 303: Electromagnetic Fields and Waves Fall 2006 Final Exam December 8, 2006 INSTRUCTIONS: • Only work done on the blue exam booklets will be graded – do not attach your own sheets to the exam booklets under any circumstances • Every problem must be done in a separate blue booklet – so you must have 5 separate blue booklets before starting the exam • To get partial credit you must show all the relevant work • Correct answers with wrong reasoning will not get points • All questions do not have the same level of difficulty DO NOT WRITE IN THIS SPACE School of Electrical and Computer Engineering, Cornell University 2 Problem 1 (20 points) Consider the transmission line circuit shown below: Assume that 3 = l m, 8 10 3 × = v m/s. The current source is a constant current source with value equal to 4 Amps and it was switched on long time ago in the past, i.e. at time −∞ = t . The switch is in the open position. a) Find and plot the currents ( ) t z I , + , ( ) t z I , − and ( ) t z I , on the transmission line for ≤ ≤ − z l . Use the attached sheet to plot your results. Partial credit will be given only if proper work is shown. At time = t the switch in the middle of the transmission line is closed shorting the transmission line at the location 2 l − = z . The switch remains closed for a period of 2 ns and then it is opened again. b) Find and plot the currents ( ) t z I , + , ( ) t z I , − and ( ) t z I , on the transmission line for ≤ ≤ − z l at time v t 4 l = . Use the attached sheet to plot your results. Partial credit will be given only if proper work is shown. Z o = 50 Ω I z = - ℓ / 2 z = 0 L 150 Ω Z o = 50 Ω z = - ℓ 150 Ω School of Electrical and Computer Engineering, Cornell University 3 Problem 2 (20 points) a) Consider a perfect metal spherical shell containing a charge dipole (i.e. two point charges, + q and - q , at the locations shown below). Find the solution ( ) r out r φ for the potential outside the spherical shell (i.e. for r ≥ a )....
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final_exam_2006 - School of Electrical and Computer...

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