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

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School of Electrical and Computer Engineering, Cornell University ECE 303: Electromagnetic Fields and Waves Fall 2005 Homework 2 Due on Sep. 09, 2005 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 dipole) Consider two equal and opposite charges sitting on the z-axis at locations 2 d z ± = , as shown in the figure below. a) Find the potential () r r at a location r r far away from the dipole (where d r >> r ). b) Find the electric field () r E r r from your result in part (a). r r z d x q + q θ 1
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Problem 2.2: (Electric dipole near a perfect metal ground plane – electric quadrupole) Consider the dipole of Problem 2.1 placed near a semi-infinite perfect metal ground plane, as show in the figure below. a) Using the method of images draw the image charges corresponding to the dipole and indicate the location and orientation and magnitude of these image charges in a sketch. b) Find the potential () r r φ outside the perfect metal for all r r in the x-z plane (i.e. for the angle in the spherical co-ordinates equal to zero). Hints:
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This note was uploaded on 09/20/2007 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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