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AP Physics C: E&M
8.6 Gauss’s Law
8.4 Electric Fields of Charge Distributions
AdvancedMCQMathematicalConceptual17.7k
Cross section of the solid insulating sphere and concentric thin shell.
Cross section of the solid insulating sphere and concentric thin shell.
A solid insulating sphere of radius \(R\) has a non-uniform volume charge density \(\rho(r) = \rho_0 \left(\dfrac{r}{R}\right)\) for \(r \le R\). The sphere is concentric with a thin conducting spherical shell of radius \(3R\) that carries a net surface charge \(Q_{\text{shell}}\). Across the surface of the outer shell at \(r = 3R\), the step change in the magnitude of the electric field, \(\Delta E = |E((3R)^+) - E((3R)^-)|\), is equal to the magnitude of the electric field at the surface of the inner solid sphere, \(E(R)\). In terms of \(\rho_0\) and \(R\), what is the magnitude of the net charge \(|Q_{\text{shell}}|\) on the outer spherical shell?

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