This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 1 School of Electrical and Computer Engineering, Cornell University ECE 303: Electromagnetic Fields and Waves Fall 2005 Homework 3 Due on Sep. 16, 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 5.0-5.3, 5.9, 6.0-6.2. 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. Solutions of Laplaces Equation Spherical Coordinate System Cylindrical Coordinate System ( ) B r A r + = Spherically symmetric potential ( ) ( ) B r A r + = ln Cylindrically symmetric potential ( ) ( ) cos r A r = Potential for uniform z- directed E-Field in spherical coordinates ( ) ( ) cos r A r = Potential for uniform x- directed E-Field in cylindrical coordinates ( ) ( ) 2 cos r A r = Potential for dipole-like solution Problem 3.1: (Meta-materials: a nano-structured dielectric medium) These days nano-technology is being used to design materials (as opposed to relying on nature) that have some desired characteristics. In this problem you will explore one such material made out of nano- dots. Consider a material made up of nano-sized dielectric spheres (or nano-dots) of dielectric permittivity 1 embedded in another material that has the same permittivity as that of free-space ( o ), as shown below. o 1 2 We will consider this problem in different steps. Consider first a single dielectric sphere of radius a and of dielectric permittivity 1 embedded in a medium of permittivity o , as shown below. A constant and uniform E-field has been applied in the +z-direction from outside. uniform E-field has been applied in the +z-direction from outside....
View Full Document
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).
- Fall '06