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AP Physics C: E&M
8.6 Gauss’s Law
8.4 Electric Fields of Charge Distributions
AdvancedMCQMathematical25k
Cross section of an infinitely long cylinder with non-uniform charge density.
Cross section of an infinitely long cylinder with non-uniform charge density.
An infinitely long, solid insulating cylinder of radius \(R\) carries a non-uniform volume charge density given by \(\rho(r) = \rho_0 \left(1 - \dfrac{r}{R}\right)\) for \(r \le R\), where \(\rho_0\) is a positive constant and \(r\) is the radial distance from the central axis. Which of the following expressions gives the magnitude of the electric field \(E(r)\) inside the cylinder as a function of \(r\) for \(r < R\)?

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