mid winter 07

mid winter 07 - The induced charge density on the top...

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EE101 2007 Winter Midterm Name: _________________________ ID: _________________________ Problem 1 (30 points) The capacitor shown in figure consists of two parallel dielectric layers ( ε 1 and ε 2 ). The bottom conductor plate is grounded and top plate is connected with voltage source V 0 . Neglect the fringing field (field does not depends on variable x, y). The area of plate is A. Please find: a). (7 oints) Electrical field (vector) distribution E (z) for the 0<=z<=a+b. b). (7 points) Potential distribution V(z). c). (5 point) The charge density and total charge Q on the top conductor plate. d). (5 points) The capacitor capacitance. e). (3 points) The electrostatic energy density. f). (3 points) Total electrostatic energy and prove it is equal to V 0 Q/2. #1 #2 #3 #4 #5 total ε 1 ε 2 b a z V 0
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Problem 2 (20 point) A line charge ρ l is place over infinite ground plane as shown in figure. Please find: a). (15 point) Electric field intensity distribution E (x, y) b). (5 point)
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Unformatted text preview: The induced charge density on the top surface of ground plane. d y x P(x, y) l Problem 3 (20 points) Assume that N turns of wire are tightly wound on toroidal frame of a rectangular cross section with dimension as shown in the Fig 3. Assume the permeability of the medium to be µ o . 1. (10 points) find the magnetic field H and magnetic flux density B inside the toroidal. (a<r<b) 2. (10 points) find the self-inductance of the toroidal Problem 4 (25 Point) The rectangular loop of N turn is coplanar with long straight wire carrying the current I. Please find: a). (5) The magnetic flux density B (r) due to straight wire ( need derivation ) b). (10) The magnetic flux though the loop c). (5) The magnetic flux linkage d). (5) The mutual inductance L 12 z I r 1 r 2 l r Problem 5 (5 Points) Prove the conductance G and capacitance of structure shown in the figure satisfy following relationship G / C = σ/ε condu ctor cond uctor ε, σ V I...
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This note was uploaded on 03/16/2010 for the course EE 101 taught by Professor Williams during the Spring '07 term at UCLA.

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mid winter 07 - The induced charge density on the top...

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