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title: "A solid conducting sphere of radius \\(R\\) carries a net positive charge \\(+Q\\) and is in electrostatic equilibrium. Let \\(E(0)\\) and \\(V(0)\\) be the electric field magnitude and electric potential at the center of the sphere, respectively, and let \\(E(R)\\) and \\(V(R)\\) be the electric field magnitude and electric potential at the surface of the sphere. Taking \\(V = 0\\) at infinity, which of the following correctly compares the electric field magnitudes and electric potentials at these two locations?"
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url: "https://nerd-notes.com/ubq/118213/"
date_modified: "2026-08-04T08:08:12+00:00"
---

# A solid conducting sphere of radius \(R\) carries a net positive charge \(+Q\) and is in electrostatic equilibrium. Let \(E(0)\) and \(V(0)\) be the electric field magnitude and electric potential at the center of the sphere, respectively, and let \(E(R)\) and \(V(R)\) be the electric field magnitude and electric potential at the surface of the sphere. Taking \(V = 0\) at infinity, which of the following correctly compares the electric field magnitudes and electric potentials at these two locations?

A solid conducting sphere of radius \(R\) carries a net positive charge \(+Q\) and is in electrostatic equilibrium. Let \(E(0)\) and \(V(0)\) be the electric field magnitude and electric potential at the center of the sphere, respectively, and let \(E(R)\) and \(V(R)\) be the electric field magnitude and electric potential at the surface of the sphere. Taking \(V = 0\) at infinity, which of the following correctly compares the electric field magnitudes and electric potentials at these two locations?

![A solid circle representing a conducting sphere of radius R, centered at the origin. The sphere is shaded light gray to indicate a conductor, with positive sign symbols (+) distributed around its outer surface. A point at the center is labeled r = 0, and a point on the outer surface is labeled r = R with a radial line segment from the center to the surface labeled R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830892-4h7DsN.jpg)

- **A.** \(E(0) = E(R)\) and \(V(0) = 0\)
- **B.** \(E(0) = E(R)\) and \(V(0) = V(R)\)
- **C.** \(E(0) < E(R)\) and \(V(0) < V(R)\)
- **D.** \(E(0) < E(R)\) and \(V(0) = V(R)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118213/*