329fall08hw2 - ECE 329 Homework 2 Due Sept 9 2008 5PM 1...

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ECE 329 Homework 2 Due: Sept 9, 2008, 5PM 1. Infinitesimal electric field at position ( x o , 0 , 0) of an infinite charge strip along the z -axis with an infinitesimal width dx along x is found to be d E = ˆ x ρ S 2 π o x o dx, where ρ S is the uniform surface charge density of the strip measured in C/m 2 units. Show that the field at the same location is E = ˆ x ρ S 2 π o ln[ x o x o - W ] if the strip has a finite width W > 0 extending from x = 0 to x = W < x o . Hint: superpose shifted versions of the expression for d E within an appropriately constructed integral. 2. Gauss’s law for electric field E states that S E · d S = 1 o V ρ dV 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 S E · d S over the surface of a cube of volume V = L 3 centered about the origin, if ρ ( x, y, z ) = 1 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.
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