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311final - ECE 311 Spring Quarter 2010 Final Exam June 9th...

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ECE 311 - Spring Quarter 2010 Final Exam June 9th, 2010 Write your name below and sign the honor pledge “No aid given, received, or observed” if it applies. There are 3 problems on this exam. Exam is open book and notes. Please box or underline your final answers, and remember to include units. Be sure to show all work clearly if you wish to obtain any partial credit. Try to keep your work within the provided space; use the back of a previous sheet if necessary. A partial list of useful formulas is included below for your reference. Name: ____________________________________________________ “The Pledge”: ____________________________________________________ Gauss’ Law (integral form) D S d ° ρ V V d = differential form: D ρ V = E field path independence E dL ° 0 = differential form: E × 0 = Potential difference: V P 2 ( ) V P 1 ( ) E l d P 1 P 2 = ε 0 8.854 10 12 × = F/m Capacitance -Definition C Q V ------ = Energy in a capacitor 1 2 -- CV 2 Dielectric media D ε E = Electrostatic boundary conditions E t 1 E t 2 = D n 1 D n 2 ρ S = Ohm’s Law J σ E = Resistance - Definition R V I --- = Uniform conductors: RC ε σ = Charge conservation (integral) J S d ° t ρ V V d = differential form: J t ρ V ( ) = Power dissipation in a volume P E J V d σ E 2 V d 1 σ --- J 2 V d = = = Definitions of curl and divergence in cylindrical and spherical coordinates: see PS 7 or book x d x n ----- a b 1 n 1 ----------- 1 a n 1 ----------- 1 b n 1 ----------- = for n>1 x d x ----- a b b a --
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