329sum09hw2sol

# 329sum09hw2sol - ECE-329 Summer 2009 Homework 2 Solution 1...

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ECE-329 Summer 2009 Homework 2 — Solution June 17, 2009 1. Infinite charge sheets. a) Displacement vector at the origin due to sheet 1 ( ρ s 1 = 1 C m 2 ) D 1 = 1 2 ρ s 1 ˆ x = 1 2 ˆ x C m 2 . Displacement vector at the origin due to sheet 2 ( ρ s 2 = 1 C m 2 ) D 2 = - 1 2 ρ s 2 ˆ x = - 1 2 ˆ x C m 2 . Resultant displacement vector due to both sheets D = D 1 + D 2 = 0 C m 2 . b) Displacement vector at the origin due to sheet 1 ( ρ s 1 = 1 C m 2 ) D 1 = 1 2 ρ s 1 ˆ x = 1 2 ˆ x C m 2 . Displacement vector at the origin due to sheet 2 ( ρ s 2 = - 2 C m 2 ) D 2 = - 1 2 ρ s 2 ˆ x = 1ˆ x C m 2 . Resultant displacement vector due to both sheets D = D 1 + D 2 = 3 2 ˆ x C m 2 . 2. Let us apply Gauss law (in integral form) ˛ S E · d S = 1 o ˆ V ρdV to compute the electric flux ¸ S E · d S over the surface of a cube of volume V = L 3 that is centered at the origin. 1

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ECE-329 Summer 2009 L 2 (1 , 1 , 1) L 2 ( - 1 , 1 , 1) L 2 ( - 1 , 1 , - 1) L 2 (1 , 1 , - 1) L 2 (1 , - 1 , - 1) L 2 (1 , - 1 , 1) L 2 ( - 1 , - 1 , 1) L 2 ( - 1 , - 1 , - 1) x y z dS 2 dS 1 dS 3 a) If the electric charge density within the cube is ρ = 1 C / m 3
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