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title: "A solid insulating sphere of radius \\(R\\) has a non-uniform volume charge density given by \\(\\rho(r) = Cr\\) for \\(r \\le R\\), where \\(C\\) is a positive constant and \\(r\\) is the radial distance from the center of the sphere. The electric potential is defined to be zero at infinity (\\(V(\\infty) = 0\\)). Which of the following expressions represents the electric potential \\(V(r)\\) inside the sphere as a function of \\(r\\) for \\(r \\le R\\)?"
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url: "https://nerd-notes.com/ubq/118135/"
date_modified: "2026-08-04T08:05:23+00:00"
---

# A solid insulating sphere of radius \(R\) has a non-uniform volume charge density given by \(\rho(r) = Cr\) for \(r \le R\), where \(C\) is a positive constant and \(r\) is the radial distance from the center of the sphere. The electric potential is defined to be zero at infinity (\(V(\infty) = 0\)). Which of the following expressions represents the electric potential \(V(r)\) inside the sphere as a function of \(r\) for \(r \le R\)?

A solid insulating sphere of radius \(R\) has a non-uniform volume charge density given by \(\rho(r) = Cr\) for \(r \le R\), where \(C\) is a positive constant and \(r\) is the radial distance from the center of the sphere. The electric potential is defined to be zero at infinity (\(V(\infty) = 0\)). Which of the following expressions represents the electric potential \(V(r)\) inside the sphere as a function of \(r\) for \(r \le R\)?

- **A.** \(\dfrac{C}{12\varepsilon_0} (R^3 - r^3)\)
- **B.** \(\dfrac{C}{4\varepsilon_0} (R^3 - r^3)\)
- **C.** \(\dfrac{C}{12\varepsilon_0} (4R^3 - r^3)\)
- **D.** \(\dfrac{C}{12\varepsilon_0} (4R^3 - 3r^3)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118135/*