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Unformatted text preview: Electromagnetics Workshop – Final Review Final Review Problems & Solutions Problem 1: A cylindrical capacitor with inner radius a and outer radius b is filled with an inhomogeneous dielectric having k ε ε ρ = , where k is a constant. Calculate the capacitance per unit length of the capacitor. Problem 1 Solution: ˆ C dS d ρ × = ∫ ∫ D n l l Ñ [ ] 2 0 0 ˆ ˆ V/m 2 k E d dz E k π ρ ρ ε ρ ρ φ ρ ρ π ε × = ⇒ = ∫ ∫ ρ ρ l l l l ( 29 [ ] V 2 2 a b b a d k k ρ ρ ρ π ε π ε- Φ = - = ∫ l l ( 29 [ ] 2 F/m k Q C b a π ε = = Φ- l l 1 Electromagnetics Workshop – Final Review Final Review Problems & Solutions Problem 2: The cross-sectional view of an air-filled coaxial capacitor with spacers made out of material with permittivity ε is shown in the figure below. (a) Find the capacitance per unit length of this coaxial line in terms of ε , a , b , and φ . (b) If the spacers are to be made out of mica ( 29 6 ε ε = , determine the angle φ such that only 10% of the total energy stored by the capacitor is stored in the spacers. (c) Consider the capacitor without the spacers (i.e....
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This note was uploaded on 10/25/2011 for the course ECE 2317 taught by Professor Staff during the Fall '08 term at University of Houston.
- Fall '08