450fall09hw3_Sol

# 450fall09hw3_Sol - ECE 450 Fall 2009 Homework 3 Solutions...

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ECE 450 Fall 2009 Homework 3 Solutions Due: Tuesday, Sep 15 th , 2009 Î See the following pages, the solutions this time are handwritten. If you have any questions please contact me <tlroach@illinois.edu>. Î For those that were in need of an “extra” exercise, a derivation of the vector potential for the small loop follows the original problem solutions. 1

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1. Problem #1 For small loop: 2 0 1 ˆ (, ) s in , 4 e rI a j k rr jkr θ φμ π π ⎛⎞ =+ ⎜⎟ ⎝⎠ A ± where, k ω μ = ε . Note, only a ˆ φ component exist which is a function of and r . a. Find and EH ±± () 2 2 0 2 2 0 ˆ 11 (s i n ) ( ) sin ˆ ˆ 1 sin sin 4s i n ˆ 1s i ˆ 2sin cos i n jkr jkr jkr jkr r Ar A r Ia re e e jk r jk r r r r r jk r φφ μμ θθ πθ −− ⎧⎫ ∂∂ ⎪⎪ ⎡⎤ =∇ ×= ⎨⎬ ⎢⎥ ⎣⎦ ⎩⎭ ˆ + HA ± ± 2 2 2 2 0 23 22 2 00 n cos 1 ˆ ˆ 2s 4 2 ˆ ˆ cos 44 jkr jkr jkr jkr jkr jkr jkr jkr jkr jkr jkr jkr jke e ke ek e j k e e rj k r r r r jke e k e jke e r r ππ
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## This note was uploaded on 02/21/2010 for the course ECE 450 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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450fall09hw3_Sol - ECE 450 Fall 2009 Homework 3 Solutions...

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