329sum09hw3 - ECE 329 Homework 3 Due 5PM 1 Consider a...

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ECE 329 Homework 3 Due: June 25, 2009, 5PM 1. Consider a three-slab geometry of three identical slabs of equal widths W in x -direction, and infinite extent in y and z directions. In slab 1 extending over - 2 W < x < - W , charge density ρ is - 2 ρ o , where ρ o measured in C/m 3 units is some positive number. In slab 2 extending over - W < x < 0 the charge density is - ρ o . Finally, in slab 3 extending over 0 < x < W the charge density is 3 ρ o . Charge density ρ is zero everywhere else. Determine and sketch E x ( x ) over the region - 3 W < x < 3 W . Label both axes of your plot carefully, marking the field value at each break point. Hint: use superposition of shifted and scaled versions of the static field configuration of a single charged slab. 2. Coulomb’s field of a charge Q stationed at the origin of a right-handed Cartesian coordinate system can be expressed as E = Q 4 π o r 2 ˆ r = Q 4 π o r 2 ( x, y, z ) r , where r 2 x 2 + y 2 + z 2 and r 0 . Verify that ∇ × E = 0 by showing that when ∇ × E is expanded as usual, all of its components cancel out exactly.
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