329sum09hw3sol

# 329sum09hw3sol - ECE-329 Summer 2009 Homework 3 —...

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Unformatted text preview: ECE-329 Summer 2009 Homework 3 — Solution June 25, 2009 1. Let us consider the static charge configuration shown in the next figure composed of three charged slabs of equal widths W in x-direction and infinite extent in y and z directions. W- W-2 W x y-2 ρ o- ρ o 3 ρ o Slab 1 Slab 2 Slab 3 The electric field generated by a single charged slab has been derived in the class notes. Making use of that result, we find that the electric fields generated by each of the three slabs depicted above are, respectively, E 1 = ρ o W o ˆ x, x <- 2 W,- 2 ρ o o ( x + 3 W 2 ) ˆ x,- 2 W < x <- W,- ρ o W o ˆ x, x >- W, W- W-2 W x-3 W 3 W 2 W E 1 x- 2 ρ o ǫ o- ρ o ǫ o 2 ρ o ǫ o ρ o ǫ o E 2 = ρ o W 2 o ˆ x, x <- W,- ρ o o ( x + W 2 ) ˆ x,- W < x < ,- ρ o W 2 o ˆ x, x > , W- W-2 W x-3 W 3 W 2 W E 2 x- 2 ρ o ǫ o- ρ o ǫ o 2 ρ o ǫ o ρ o ǫ o 1 ECE-329 Summer 2009 E 3 = - 3 ρ o W 2 o ˆ x, x < , 3 ρ o o ( x- W 2 ) ˆ x, < x < W, 3 ρ o W 2 o ˆ x, x > W. W- W-2 W x-3 W 3 W 2 W E 3 x- 2 ρ o ǫ o- ρ o ǫ o 2 ρ o ǫ o ρ o ǫ o Adding these fields, we find that the total field in space is E = E 1 + E 2 + E 3 = - 2 ρ o o ( x + 2 W ) ˆ x,- 2 W < x <- W,- ρ o o ( x + 3 W ) ˆ x,- W < x < , 3 ρ o o ( x- W ) ˆ x, < x < W,...
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329sum09hw3sol - ECE-329 Summer 2009 Homework 3 —...

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