homework2 - School of Electrical and Computer Engineering,...

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1 School of Electrical and Computer Engineering, Cornell University ECE 303: Electromagnetic Fields and Waves Fall 2007 Homework 2 Due on Sep. 07, 2007 by 5:00 PM Reading Assignments: i) Review the lecture notes. ii) Relevant sections of the online Haus and Melcher book for this week are 4.0-4.6. Note that the book contains more material than you are responsible for in this course. Determine relevance by what is covered in the lectures and the recitations. The book is meant for those of you who are looking for more depth and details. Spherically or Cylindrically Symmetric Solutions of Laplace’s Equation Spherical Coordinate System Cylindrical Coordinate System () B r A r + = φ ( ) ( ) B r A r + = ln Problem 2.1: (Electric charge above a perfect metal strip) Consider a point charge sitting on the z-axis at location 2 d z + = above an infinite perfect metal strip (infinite in the x-y plane and of thickness 4 d ), as shown in the figure below. a) Find the potential () r r outside the perfect metal at a location r r far away from the charge (where d r >> r ). Use spherical coordinates. You need to find the potential for both 0 < z and 0 > z . b) Find the electric field () r E r r from your result in part (a). 2 d x z q + r r θ perfect metal strip 4 d
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2 c) Find the position dependent surface charge density (units: Coulombs/m 2 ) on the upper and lower surfaces of the metal strip. d) From your answer in part (c) find the total charge (units: Coulombs) on the upper surface of the metal strip. Problem 2.2: (Electric charge near perfect metal planes) Consider a point charge placed near the corner of perfect metal planes, as show in the figure below. The metal planes are infinite in the y-direction. The point charge is placed at 0 = y . a) Using the method of images draw the image charges corresponding to the point charge and indicate the
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This note was uploaded on 09/02/2008 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell University (Engineering School).

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homework2 - School of Electrical and Computer Engineering,...

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