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title: "A solid conducting sphere of radius \\(R\\) carries a net positive charge \\(+Q\\) and is in electrostatic equilibrium in free space. The electric potential is defined to be zero at an infinite distance from the sphere (\\(V(\\infty) = 0\\)). Which of the following graphs best represents the electric potential \\(V\\) as a function of radial distance \\(r\\) from the center of the sphere?"
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url: "https://nerd-notes.com/ubq/121095/"
date_modified: "2026-08-23T04:57:49+00:00"
---

# A solid conducting sphere of radius \(R\) carries a net positive charge \(+Q\) and is in electrostatic equilibrium in free space. The electric potential is defined to be zero at an infinite distance from the sphere (\(V(\infty) = 0\)). Which of the following graphs best represents the electric potential \(V\) as a function of radial distance \(r\) from the center of the sphere?

A solid conducting sphere of radius \(R\) carries a net positive charge \(+Q\) and is in electrostatic equilibrium in free space. The electric potential is defined to be zero at an infinite distance from the sphere (\(V(\infty) = 0\)). Which of the following graphs best represents the electric potential \(V\) as a function of radial distance \(r\) from the center of the sphere?

- **A.** A graph where \(V(r) = 0\) for \(0 \le r < R\), with a discontinuous jump at \(r = R\) to a curve that decays asymptotically toward zero for \(r > R\).
- **B.** A graph where \(V(r)\) increases linearly from zero at \(r = 0\) to a peak value at \(r = R\), followed by a curve that decays asymptotically toward zero for \(r > R\).
- **C.** A graph where \(V(r)\) decreases linearly from a maximum at \(r = 0\) to a non-zero value at \(r = R\), followed by a curve that decays asymptotically toward zero for \(r > R\).
- **D.** A graph where \(V(r)\) is constant and non-zero for \(0 \le r \le R\), followed by a smooth, continuous curve that decays asymptotically toward zero as \(1/r\) for \(r > R\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121095/*