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AP Physics C: E&M
8.6 Gauss’s Law
8.4 Electric Fields of Charge Distributions
AdvancedMCQMathematical23.6k
Cross-sectional view of concentric spherical regions centered at the origin. At the center is a solid shaded circle of radius R labeled with charge density \rho_1(r) = \rho_0(r/R). Surrounding it is a region of empty space extending from radius R to 2R. Next is a thick spherical shell extending from inner radius 2R to outer radius 3R, filled with hatch lines and labeled with charge density \rho_2(r) = -\rho_0(R/r). A dashed circular Gaussian surface of radius r sits in the region between 2R and 3R. A radial arrow from the origin to the dashed circle is labeled r. No other labels, lines, text, or axes appear.
Cross-section of the concentric solid sphere and thick insulating shell.
A solid insulating sphere of radius \(R\) contains a non-uniform volume charge density \(\rho_1(r) = \rho_0 \left(\dfrac{r}{R}\right)\), where \(\rho_0\) is a positive constant and \(r\) is the radial distance from the center. Concentric with this sphere is a thick insulating spherical shell with inner radius \(2R\) and outer radius \(3R\). The thick shell contains a non-uniform volume charge density \(\rho_2(r) = -\rho_0 \left(\dfrac{R}{r}\right)\). Which of the following expressions correctly gives the magnitude of the electric field \(E(r)\) in the region \(2R < r < 3R\) as a function of \(r\)?

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