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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 1.11.6 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 EField in spherical coordinates ( ) ( ) φ φ cos r A r = r Potential for uniform x directed EField in cylindrical coordinates ( ) ( ) 2 cos r A r θ φ = r Potential for pointcharge dipolelike solution with the dipole pointing in the +zdirection ( ) ( ) r A r φ φ cos = r Potential for a linecharge dipolelike solution with the dipole pointing in the +xdirection Problem 5.1: (Force on charged biomolecules in microfluidics) In many cases of practical interest relating to onchip biomolecule analysis, biomolecules together with some fluid are flown in narrow integrated microfluidic 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
 RANA
 Electromagnet, Electric charge, Coordinate system, plane waves, perfect metal, metal ground plane

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