450fall09hw2 - ECE 450 Homework 2 Due: Tue, Sept 8, 2009, 5...

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ECE 450 Homework 2 Due: Tue, Sept 8, 2009, 5 PM 1. Consider the time-harmonic charge distribution ρ ( r ,t )= q [ δ ( r - h ˆ x ) - δ ( r + h ˆ x )+ δ ( r - h ˆ y ) - δ ( r + h ˆ y )] cos( ωt ) C m 3 in free space. a) Write down the phasors for the charge density ρ ( r ,t ) and its time derivative ∂ρ ∂t . b) Calculate the divergence ∇· J of the current density associated with ρ ( r ,t ) above. Hint: conti- nuity equation. c) What is the retarded scalar potential phasor ˜ V generated by ρ ( r ,t ) above? 2. Give the time-harmonic expressions with the frequency ω for the Felds A ( r ,t ) with the following phasors: a) ˜ A ( r )= j x - y b) ˜ A ( r )= ˆ y +2 ω 2 ˆ z c) ˜ A ( r )=( j ˆ x +2ˆ y ) e - jkz where k is a constant. 3. Consider the time-harmonic vector Feld A ( r ,t )=ˆ xA x ( r )cos( ωt + φ x ( r )) + ˆ yA y ( r )cos( ωt + φ y ( r )) + ˆ zA z ( r )cos( ωt + φ z ( r )) . a) Show that its complex valued phasor
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This note was uploaded on 02/22/2010 for the course ECE 450 taught by Professor Franke during the Fall '09 term at University of Illinois at Urbana–Champaign.

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450fall09hw2 - ECE 450 Homework 2 Due: Tue, Sept 8, 2009, 5...

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