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329sp09hw2(2) - ECE 329 Homework 2 Due Feb 3 2009 5PM 1...

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ECE 329 Homework 2 Due: Feb 3, 2009, 5PM 1. Charges Q 1 = 8 π o C and Q 2 = - Q 1 / 2 are located at points P 1 and P 2 having the position vectors r 1 = - ˆ x = - (1 , 0 , 0) m and r 2 = ˆ x = (1 , 0 , 0) m, respectively. Determine the electric field vector E at points P 3 and P 4 having the position vectors r 3 = ˆ y = (0 , 1 , 0) m and r 4 = ˆ z = (0 , 0 , 1) m, respectively. Make sketches showing the charge locations and the resulting electric field vectors (drawn coming out of points P 3 and P 4 , respectively) in each case. 2. An infinite charge strip along the z -axis with an infinitesimal width dx along x produces an infinites- imal electric field d E = ˆ x ρ S 2 π o x o dx at ( x o , 0 , 0) , where ρ S denotes the uniform surface charge density of the strip in C/m 2 units. Show that the field at the same location would be E = ˆ x ρ S 2 π o ln[ x o x o - W ] if the strip had a finite width W > 0 extending from x = 0 to x = W < x o . Hint: superpose shifted versions of d E within an appropriately constructed integral. 3. 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 .
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