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AP Physics C: E&M
8.6 Gauss’s Law
8.4 Electric Fields of Charge Distributions
IntermediateMCQMathematical14.5k
Cross section of a non-uniformly charged sphere with a concentric Gaussian surface of radius r.
Cross section of a non-uniformly charged sphere with a concentric Gaussian surface of radius r.
A solid insulating sphere of radius \(R\) contains a total net charge \(Q\). The volume charge density \(\rho\) inside the sphere varies directly with radial distance \(r\) from the center, such that \(\rho(r) = C r\) for \(r \le R\), where \(C\) is a constant. In terms of \(Q\), \(R\), \(r\), and fundamental constants, which of the following expressions represents the magnitude of the electric field at a distance \(r < R\) from the center of the sphere?

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