450sp11hw2 - ECE 450 Homework 2 Due: Tue, Feb 1, 2011, 5 PM...

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Unformatted text preview: ECE 450 Homework 2 Due: Tue, Feb 1, 2011, 5 PM 1. a) Given the vector potential A , the magnetic fux density is B = A (by deFnition). Express the closed path integral C A d l around a path C in terms o the integral o B over a surace bounded by path C . Hint: make use o Stokes thm (Lecture 6, ECE 329 notes). b) Given the static current density J ( r ) = zJ s ( x ) , where J s is a constant, it is known that B ( r ) = y o J s 2 sgn ( x ) (see Lect 13, ECE 329 notes). Determine the corresponding vector potential A ( r ) in the Coulomb gauge (i.e., A = 0) . Hint: make use o the result o part (a) and the act that direction o A is the same as the direction o J . 2. a) Give the time-harmonic expressions with the requency or the Felds A ( r , t ) with the ollowing phasors: i. A ( r ) = j x-2 y ii. A ( r ) = x + j y + 2 2 z = x + j y-2( j ) 2 z iii. A ( r ) = (2 x + j 2 y ) e-jkz where k is a positive constant. Recall that a phasor is converted to the time-harmonic expression by multiplying it with e jt and taking the real part o the product....
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This note was uploaded on 08/25/2011 for the course ECE 350 taught by Professor Kudeki during the Spring '11 term at University of Illinois at Urbana–Champaign.

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450sp11hw2 - ECE 450 Homework 2 Due: Tue, Feb 1, 2011, 5 PM...

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