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Unformatted text preview: 1 School of Electrical and Computer Engineering, Cornell University ECE 303: Electromagnetic Fields and Waves Fall 2005 Homework 5 Due on Sep. 30, 2005 by 5:00 PM Reading Assignments: i) Review the lecture notes. ii) Review sections 1.1-1.6 of the paperback book Electromagnetic Waves . Solutions of Laplace’s Equation for ECE303 Spherical Coordinate System Cylindrical Coordinate System ( ) A r = φ Constant potential ( ) A r = φ Constant potential ( ) r A r = φ Spherically symmetric potential ( ) ( ) r A r ln = φ Cylindrically symmetric potential ( ) ( ) θ φ cos r A r = r Potential for uniform z- directed E-Field in spherical coordinates ( ) ( ) φ φ cos r A r = r Potential for uniform x- directed E-Field in cylindrical coordinates ( ) ( ) 2 cos r A r θ φ = r Potential for point-charge- dipole-like solution with the dipole pointing in the +z-direction ( ) ( ) r A r φ φ cos = r Potential for a line-charge- dipole-like solution with the dipole pointing in the +x-direction Problem 5.1: (Force on charged bio-molecules in micro-fluidics) In many cases of practical interest relating to on-chip bio-molecule analysis, bio-molecules together with some fluid are flown in narrow integrated micro-fluidic channels. One problem encountered in such experiments is that when molecules are charged they get attracted to the side walls of the channels and get...
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- Fall '06
- Electromagnet, Electric charge, Coordinate system, plane waves, perfect metal, metal ground plane