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AP Physics C: E&M
8.6 Gauss’s Law
8.5 Electric Flux
8.4 Electric Fields of Charge Distributions
AdvancedMCQGraphicalMathematicalConceptual18.6k
A shaded circular disk representing a solid sphere of radius R is centered at an origin. A solid double-ended arrow labeled R extends from the center to the outer perimeter of the shaded sphere at an angle of 35 degrees above the horizontal. A dashed circular line concentric with the sphere represents a Gaussian surface of radius r, shown with r < R. A dashed arrow labeled r extends from the center to the dashed circle at an angle of 35 degrees below the horizontal. No other labels, lines, text, or axes appear.
Solid sphere of radius R with concentric Gaussian surface of radius r.
A solid insulating sphere of radius \(R\) is centered at the origin and has a non-uniform volume charge density given by \(\rho(r) = C r\) for \(r \le R\), where \(C\) is a positive constant and \(r\) is the radial distance from the center. Outside the sphere (\(r > R\)), the charge density is zero. Which of the following graphs best represents the electric flux \(\Phi_E\) through a concentric spherical Gaussian surface as a function of its radius \(r\)?

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