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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 <[email protected]>. 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 ( , ) sin , 4 e r I a jk r r jkr θ φ μ π θ π = + A ± where, k ω μ = ε . Note, only a ˆ φ component exist which is a function of and r θ . a. Find and E H ± ± ( ) 2 2 0 2 2 0 ˆ 1 1 ( sin ) ( ) sin ˆ ˆ 1 sin sin 4 sin ˆ 1 si ˆ 2sin cos 4 sin jkr jkr jkr jkr r A rA r r r I a r e e e jk r jk r r r r r r r I a r e jk r r r φ φ θ θ μ μ θ θ π θ θ θ π θ θ π θ θ θ π θ = ∇× = ˆ = + +
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450fall09hw3_Sol - ECE 450 Fall 2009 Homework 3 Solutions...

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