Electrical Engineering 117A - Fall 1995 - Neureuther - Final - EECS 117A Final Fall 1995 EECS 117A Fall 1995 Final Exam Professor A.R Neureuther

Electrical Engineering 117A - Fall 1995 - Neureuther -...

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EECS 117A, Final, Fall 1995 EECS 117A, Fall 1995 Final Exam Professor A.R. Neureuther Problem #1 (70 Points) Concepts from Electrostatics, Magnetostatics and Maxwell's Equations A coaxial transmission line consists of an inner perfect electric conductor of radius a , a material inner lining from a < r < b , and an outer perfect electrical conductor of radius c . The material lining has U r = 10 and E r = 4. The dimensions a , b , and c are 2, 4, and 6 mm respectively. I.a. (20 Points) Find the magnetic flux density vector B at the radius r of 3 mm and 8 mm when a current of 1 mA flows in the inner conductor and a current of 0.5 mA flows in the opposite direction in the outer conductor. I.b. (25 Points) Using Stoke's Theorem show how to derive an equation for the change in voltage with position down the transmission line as a function of the change in current with time. Identify in your derivation and algebraic expression for the inductance per unit length. Hint: Start with a sketch of the geometry and mathematical construct. I.c. (25 Points) State if the line is despersive and or lossy and give an expression for the phase velocity as a function of the angular frequency w, radial dimensions and material properties.
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