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 12.0cmb=and inner radius 6.0cma=. The insulating material of the shell carries a uniform charge density of 332.0μC / mρ=. Use Gauss’ Law to determine a formula for the electric field strength at a distance rfrom 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: 0encEqεΦ=Left-hand side: By symmetry, everywhere on the Gaussian surface, the E-field has constant magnitude and is perpendicular to the surface (parallel to dAG). Thus, as always for spherical symmetry, 24ErrAEr Eπ=Right-hand side: The volume of the object (vertical lines in this picture) that is
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