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AP Physics C: E&M
9.2 Electric Potential
AdvancedMCQMathematicalConceptual20.9k
Cross-section of a sphere of radius \(R\) with non-uniform radial charge density.
Cross-section of a sphere of radius \(R\) with non-uniform radial charge density.
A solid non-conducting sphere of radius \(R\) has a non-uniform volume charge density given by \(\rho(r) = \rho_0\left(1 - \dfrac{r}{R}\right)\) for \(r \le R\) and \(\rho(r) = 0\) for \(r > R\), where \(\rho_0\) is a positive constant and \(r\) is the distance from the center of the sphere.

The electric potential is defined to be zero at an infinite distance from the sphere (\(V(\infty) = 0\)).

Which of the following expressions represents the electric potential \(V(r)\) at a distance \(r < R\) from the center of the sphere?

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