329sp09hw4(2) - ECE 329 Homework 4 Due: Feb 17, 2009, 5PM...

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Unformatted text preview: ECE 329 Homework 4 Due: Feb 17, 2009, 5PM 1. Curl and divergence exercises: a) On a 25-point graph consisting of x and y coordinates having the integer values {- 2 ,- 1 , , 1 , 2 } sketch the vector field F = x ˆ x + y ˆ y and find ∇× F (curl of F ) and ∇· F (divergence of F ). b) Repeat (a) for F = y ˆ x- x ˆ y . c) Based on above results choose the correct answer in the statements below: i. ∇× F = 0 implies the field strength varies ( along or across ) the direction of the field. ii. ∇· F = 0 implies the field strength varies ( along or across ) the direction of the field. 2. According to Maxwell’s equations, the divergence and curl of magnetic field vector B have to be zero in regions where the current density J and the displacement current density ∂ D ∂t are both zero. Which of the following vector fields would satisfy these conditions and thus could be realized as a magnetic field in such regions? (a) F a = (2 x + 3 y ) ˆ x + (3 x- 2 y ) ˆ y , (b) F b = x 2 y ˆ x + y 2 x ˆ y , (c) F c = y ˆ x- x ˆ y . 3. In a source-free region where J = ρ = 0 Gauss’s, Faraday’s and Ampere’s laws reduce to ∇· E = 0 , ∇× E =- ∂ B ∂t , and ∇× B = μ o o ∂ E ∂t ....
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This note was uploaded on 11/16/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.

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329sp09hw4(2) - ECE 329 Homework 4 Due: Feb 17, 2009, 5PM...

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