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aee1_midterm_ss2005 - AEE1 Midterm Exam Oct-21-2005 Prof S...

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AEE1 Midterm Exam Oct-21-2005 Prof. S. Peik AEE1 Midterm Exam Fall Term 2005 Duration: 75 min Allowed Aids: - Calculator - Formulary Please Note: - Document all Calculations - Underbar Results - Mark every page with page number and name - Hand in this title page Name: ID-#.: Problem 1 2 3 4 Max. Points 6 9 8 4 Points earned Total Points: of 27 Final Mark: Problem 1: A semi-infinite long line charge with the line charge density λ ( x ) = λ 0 extends on the x-axis from - to 0. The medium is vaccuum. x y x E=? λ (x) 1. Find the E-field ~ E on the x-axis for x > 0. Hint: R 1 ( a - x ) 2 = - 1 x - a Problem 2: A dielectric sphere with ε r = 4 and radius R is charged with the volume charge density ρ ( r ) . Inside the sphere we measure an electric flux density of ~ D = D 0 r 2 ˆ r (1) Use a spherical coordinate system. x R 1. Derive the charge density ρ ( r ) inside the sphere. 2. Find the total charge Q of the sphere as a function of D 0 and R . 3. Find the potential function V ( r ) inside the sphere. Assume a zero potential in the origin , i.e. V ( 0 ) = 0V.
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