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Midterm%20Exam%201%20Solutions

# Midterm%20Exam%201%20Solutions - Physics 11b Midterm Exam I...

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Physics 11b: Midterm Exam I with Solutions March 13, 2008 Name: Please place a check next to your section leader: Ognjen Ilic Subhaneil Lahiri Josh Lapan Daniyar Nurgaliev Roberto Martinez Problem Score Total Points 1 15 2 15 3 15 4 15 5 15 6 15 Total Score: / 90 1

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Problem 1 1. Two nonconducting spherical shells are fixed in place on the x -axis. Shell 1 has uniform surface charge density +6.0 μ C m - 2 on its outer surface and radius 3.0 cm; shell 2 has uniform surface charge density +4.0 μ C m - 2 on its outer surface and radius 2.0 cm; the shell centers are separated by L = 10 cm (shell 1 is at the origin, shell 2 on the positive x -axis). Sketch the ar- rangement. In unit-vector notation, what is the net electric field at x = 2 . 0 cm? (Solution) A shell of uniform charge creates an electric field outside of the shell as if all the shell’s charge were concentrated at the center. The electric field inside of the shell is zero. The point in question is inside the first shell (which means that electric field due to shell 1 is E 1 = 0 V m - 1 ), and outside the second shell ( E 2 = 1 4 π 0 Q 2 ( L - x ) 2 ). The area of the sphere is A = 4 πR 2 so it has a charge Q 2 = σA = 4 πσR 2 , where σ is the charge density. Hence, E = E 1 + E 2 = 1 4 π 0 4 πσR 2 ( L - x ) 2 = σR 2 0 ( L - x ) 2 = 2 . 8 × 10 4 V m - 1 The direction of the field is in the - ˆ x -direction: E = - 2 . 8 × 10 4 V m - 1 ˆ x . Problem 2 How much work is required to set up the arrangement shown in the figure below, if particles are initially infinitely far apart and at rest? Express your answer in terms of a and q .
1 3 4 2 a a a a l q q - q - q (Solution) Consider the above configuration of charged points. Note that

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Midterm%20Exam%201%20Solutions - Physics 11b Midterm Exam I...

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