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329sum11hw2 - ECE 329 Homework 2 Due 5PM 1 Gauss’s law...

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Unformatted text preview: ECE 329 Homework 2 Due: June 21, 2011, 5PM 1. Gauss’s law for electric field E states that S E · d S = 1 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 S E · d S over the surface of a cube of volume V = L 3 centered about the origin, if ρ ( x,y,z ) =- 2 C/m 3 within V and L = 1 m? b) Repeat (a) for ρ ( x,y,z ) = x 2 + y 2 + z 2 C/m 3 . c) What is the electric flux in part (b) for any one of the square surfaces of volume V ? 2. Two unknown charges, Q 1 and Q 2 are located at ( x,y,z ) = (1, 0, 0) and (-1, 0, 0), respectively, as shown below. The displacement flux yz- plane D · ˆ xdydz through the entire yz-plane in the +ˆ x direction is 2 C. The flux through the plane y = 1 in the +ˆ y direction is -3 C. Determine Q 1 and Q 2 after writing a pair of algebraic equations relating the above displacement fluxes to Q 1 and Q 2 . Hint: What is the contribution of Q 1 to the flux yz- plane D · ˆ xdydz ? See Example 5 in Lecture 3. 3. An infinite charge sheet with uniform charge density ρ s C m 2 produces electrostatic fields E with ρ s 2 o magnitude pointing away from the sheet on both sides. Also, superposition can be used to calculatemagnitude pointing away from the sheet on both sides....
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329sum11hw2 - ECE 329 Homework 2 Due 5PM 1 Gauss’s law...

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