# hw2 - ECE 329 Homework 2 Due Sept 7 2010 5PM 1 Gauss law...

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ECE 329 Homework 2 Due: Sept. 7, 2010, 5PM 1. Gauss’ law for electric field E states that H S E · d S = 1 ϵ o V ρdV over any closed surface S enclosing a volume V in which electric charge density is specified by ρ ( x, y, z ) C/m 3 . a) What is the electric ﬂux H S E · d S over the surface of a cube of volume V = L 3 centered about the origin, if ρ ( x, y, z ) = 3 C/m 3 within V ? b) Repeat (a) for ρ ( x, y, z ) = x 2 + y 2 + z 2 C/m 3 and L = 1 m. c) What is the electric ﬂux in part (b) for any one of the square surfaces of volume V ? 2. Consider two infinite parallel slabs having equal widths W and equal but opposite charge densities. Slab 1 is parallel to the xy -plane and extends from z = 2 W to z = W and has a positive uniform charge density ρ 0 C/m 3 while slab 2 extends from z = W to z = 2 W . The charge density is zero everywhere else. a) Determine and sketch the electric field component E z in terms of ρ 0 over the region 3 W < z < 3 W

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