Quiz2S - Name_SOLUTIONS Physics 125 Analytical Physics II...

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Name____ SOLUTIONS _______ Physics 125: Analytical Physics II Quiz 2/20/08 The picture shows the cross-section of a thick spherical shell, with outer radius 12.0cm b = and inner radius 6.0cm a = . The insulating material of the shell carries a uniform charge density of 3 32.0μC / m ρ = . Use Gauss’ Law to determine a formula for the electric field strength at a distance r from the center, where arb << . Your answer should be a function of r , but all parameters in the function should be numerically evaluated. Choose a Gaussian surface: a sphere of radius r (has the same symmetry as the charge, and passes through the point where we want to know the field). Apply Gauss’ Law: 0e n c E q ε Φ= Left-hand side: By symmetry, everywhere on the Gaussian surface, the E-field has constant magnitude and is perpendicular to the surface (parallel to dA G ). Thus, as always for spherical symmetry, 2 4 Er r AE r E π = Right-hand side: The volume of the object (vertical lines in this picture) that is
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