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329fall09hw2 - ECE 329 Homework 2 Due September 8 2009 5 PM...

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ECE 329 Homework 2 Due: September 8, 2009, 5 PM 1. Gauss’ Law for electric field E states that S E · dS = 1 0 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 total electric flux S E · dS through the surface of a cube of volume V = 1 m 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 . c) What is the electric flux E · dS through any one of the square surfaces of volume V for the charge density given in part (b)? 2. Two unknown charges, Q 1 and Q 2 are located along the ˆ x axis at ( x, y, z ) = (1 , 0 , 0) and at ( - 1 , 0 , 0) , respectively. The displacement flux D · dS through the entire ˆ y - ˆ z plane at x = 0 in the x direction is -2 C, while the displacement flux through the ˆ x - ˆ z plane at y = 1 in the y direction is 6 C. Determine the magnitude of charges Q 1 and Q 2 by solving a pair of algebraic equations relating the given displacement fluxes to the unknown charges.
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