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AP Physics C: E&M
8.6 Gauss’s Law
8.4 Electric Fields of Charge Distributions
AdvancedMCQMathematical16.1k
Cross-section of a non-uniform spherical shell and a Gaussian surface at radius r.
Cross-section of a non-uniform spherical shell and a Gaussian surface at radius r.
A thick, non-conducting spherical shell has an inner radius \(R\) and an outer radius \(2R\). The shell has a non-uniform volume charge density \(\rho(r) = \rho_0 \left(\dfrac{r}{R}\right)\) for \(R < r < 2R\), where \(\rho_0\) is a positive constant and \(r\) is the distance from the center of the shell. The region \(r < R\) is empty. Which of the following expressions represents the magnitude of the electric field \(E\) at a distance \(r\) from the center, where \(R < r < 2R\)?

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