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title: "Two solid conducting spheres, \\(A\\) and \\(B\\), with radii \\(R\\) and \\(2R\\) respectively, are separated by a distance much larger than \\(2R\\) and connected by a thin conducting wire. The system is in electrostatic equilibrium with a net positive charge. Which of the following correctly compares the electric potentials \\(V_A\\) and \\(V_B\\) at the surfaces of the spheres and gives the ratio of their surface charge densities \\(\\dfrac{\\sigma_A}{\\sigma_B}\\)?"
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url: "https://nerd-notes.com/ubq/118230/"
date_modified: "2026-08-04T08:08:16+00:00"
---

# Two solid conducting spheres, \(A\) and \(B\), with radii \(R\) and \(2R\) respectively, are separated by a distance much larger than \(2R\) and connected by a thin conducting wire. The system is in electrostatic equilibrium with a net positive charge. Which of the following correctly compares the electric potentials \(V_A\) and \(V_B\) at the surfaces of the spheres and gives the ratio of their surface charge densities \(\dfrac{\sigma_A}{\sigma_B}\)?

Two solid conducting spheres, \(A\) and \(B\), with radii \(R\) and \(2R\) respectively, are separated by a distance much larger than \(2R\) and connected by a thin conducting wire. The system is in electrostatic equilibrium with a net positive charge. Which of the following correctly compares the electric potentials \(V_A\) and \(V_B\) at the surfaces of the spheres and gives the ratio of their surface charge densities \(\dfrac{\sigma_A}{\sigma_B}\)?

- **A.** \(V_A = V_B\) and \(\dfrac{\sigma_A}{\sigma_B} = \dfrac{1}{2}\)
- **B.** \(V_A = V_B\) and \(\dfrac{\sigma_A}{\sigma_B} = 2\)
- **C.** \(V_A = 2V_B\) and \(\dfrac{\sigma_A}{\sigma_B} = 1\)
- **D.** \(V_A = \dfrac{1}{2}V_B\) and \(\dfrac{\sigma_A}{\sigma_B} = 4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118230/*