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final_exam_fa07

final_exam_fa07 - School of Electrical and Computer...

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School of Electrical and Computer Engineering, Cornell University 1 ECE 303: Electromagnetic Fields and Waves Fall 2007 Final Exam December 12, 2007 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 • To get partial credit you must show all the relevant work • Correct answers with wrong reasoning will not get points • All questions/parts do not carry equal points • All questions do not have the same level of difficulty DO NOT WRITE IN THIS SPACE

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School of Electrical and Computer Engineering, Cornell University 2 Problem 1 (20 points) a) Consider a thin cylindrical shell of length L and radius R located with its center at the origin and oriented along the z-direction, as shown in the figure below. The surface of the cylinder carries a surface current density (units: Amps/m) given by φ ˆ K K = r . Find the exact magnetic field vector (magnitude and direction) at the point P which is located at a distance d from the origin along the z-direction, as shown in the figure above. You may leave your answer in the form of a definite integral. b) Consider a circular loop of line charge of radius a and carrying a charge density + λ per unit length, as shown below. The loop is positioned at a distance d along the z-axis from the x-y plane and is oriented parallel to the x-y plane. The infinite space for all negative values of the coordinate z is occupied by a medium of permittivity ε . Find the exact electric field vector (magnitude and direction) at the point P which is located at a distance d from the origin along the z-direction, as shown in the figure above. You may leave your answer in the form of a definite integral. d x y z + λ L ε a P - L / 2 L / 2 y z 2R K P d L
School of Electrical and Computer Engineering, Cornell University 3 Problem 2 (20 points) Consider a short dipole of physical length d , pointing in the z-direction, carrying a current phasor I , and located at ( ) 0 , , h h in the ( ) z y x , , coordinate system, as shown in the figure below. The space for which 0 < x or 0 < y is filled with a perfect metal. a) Find the expression for the far-field electric field vector ( ) r E ff r r of the radiation and explain your result.

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final_exam_fa07 - School of Electrical and Computer...

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