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**Unformatted text preview: **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 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 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 + 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 . 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 + L 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 ( ) , , h h in the ( ) z y x , , coordinate system, as shown in the figure below. The space for which < x or < 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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