# 305_exam_2_04 - The volume charge density in free space in...

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ECE 305 Name: Spring 2004 Exam #2 Student No. Note: Be sure to include units where appropriate! Note: YOU MUST SHOW YOUR WORK TO GET CREDIT! Note: Each problem is worth 8 points 1. Stub tuning. A load with impedance 25 25 L Z j = + Ω is matched to a 50 Ω transmission line by attaching an open-circuited 50 Ω stub of length in series with the T-line a distance d from the load. Using the attached Smith chart find the smallest value of d and the resulting length . BE SURE TO SHOW YOUR WORK ON THE ATTACHED SMITH CHART!

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2. Electric Field Calculation. A line charge with constant density 0 ρ lies along a circle of radius a in the x-y plane. (a) Draw a picture and determine the direction of E a at the point (0,0,z). (b) Set up the integral for E a at the point (0,0,z).
2 continued) (c) Calculate the non-zero component of E a at the point (0,0,z).

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3. Gauss’ law.

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Unformatted text preview: The volume charge density in free space in spherical coordinates is given by , 0, v r r a a r a ρ ≤ = > a) Draw a picture and determine the direction of E a and the dependence of E a on the coordinate variables ( , , ) r θ φ . 3 continued b) Use the integral form of Gauss’ law to find E a in the region r a ≤ . 4. Potential. The electric field in rectangular coordinates in free space is given by ˆ, ˆ, , a z z a z E z a z a a z a ρ ε > =- ≤ ≤ -< - a a) Find the volume charge density v everywhere. b) Verify the boundary condition on normal D a at z a = . (Note: s = at z a = ) 4 continued b) Find the potential difference between a point at z a = and a point at z = ....
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305_exam_2_04 - The volume charge density in free space in...

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