---
title: "Two widely separated solid conducting spheres, Sphere 1 of radius \\(R\\) and Sphere 2 of radius \\(2R\\), are connected by a long, thin conducting wire so that both spheres reach the same electrostatic potential \\(V_0\\) relative to infinity. The distance between the spheres is very large compared to \\(2R\\), so mutual electrostatic induction between them is negligible. Let \\(Q_1\\), \\(\\sigma_1\\), and \\(E_1\\) represent the net charge, the surface charge density, and the magnitude of the electric field just outside the surface of Sphere 1, respectively. Which of the following correctly compares the net charge \\(Q_2\\), the surface charge density \\(\\sigma_2\\), and the electric field magnitude \\(E_2\\) just outside the surface of Sphere 2 to the corresponding quantities for Sphere 1?"
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url: "https://nerd-notes.com/ubq/124680/"
date_modified: "2026-09-28T14:09:04+00:00"
---

# Two widely separated solid conducting spheres, Sphere 1 of radius \(R\) and Sphere 2 of radius \(2R\), are connected by a long, thin conducting wire so that both spheres reach the same electrostatic potential \(V_0\) relative to infinity. The distance between the spheres is very large compared to \(2R\), so mutual electrostatic induction between them is negligible. Let \(Q_1\), \(\sigma_1\), and \(E_1\) represent the net charge, the surface charge density, and the magnitude of the electric field just outside the surface of Sphere 1, respectively. Which of the following correctly compares the net charge \(Q_2\), the surface charge density \(\sigma_2\), and the electric field magnitude \(E_2\) just outside the surface of Sphere 2 to the corresponding quantities for Sphere 1?

Two widely separated solid conducting spheres, Sphere 1 of radius \(R\) and Sphere 2 of radius \(2R\), are connected by a long, thin conducting wire so that both spheres reach the same electrostatic potential \(V_0\) relative to infinity. The distance between the spheres is very large compared to \(2R\), so mutual electrostatic induction between them is negligible. Let \(Q_1\), \(\sigma_1\), and \(E_1\) represent the net charge, the surface charge density, and the magnitude of the electric field just outside the surface of Sphere 1, respectively. Which of the following correctly compares the net charge \(Q_2\), the surface charge density \(\sigma_2\), and the electric field magnitude \(E_2\) just outside the surface of Sphere 2 to the corresponding quantities for Sphere 1?

![Two solid circular outlines representing spherical conductors are horizontally separated in a single view. The left circle, labeled Sphere 1, has radius R indicated by a horizontal line segment from its center to its right edge labeled R. The right circle, labeled Sphere 2, has twice the radius of Sphere 1, with radius 2R indicated by a horizontal line segment from its center to its right edge labeled 2R. A single thin horizontal line connects the right edge of Sphere 1 to the left edge of Sphere 2, representing a thin conducting wire. Both circular outlines have an identical uniform light gray fill. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604543-rle8LG.jpg)

- **A.** \(Q_2 = Q_1\) | \(\sigma_2 = \dfrac{1}{4}\sigma_1\) | \(E_2 = \dfrac{1}{4}E_1\)
- **B.** \(Q_2 = 4Q_1\) | \(\sigma_2 = \sigma_1\) | \(E_2 = E_1\)
- **C.** \(Q_2 = 2Q_1\) | \(\sigma_2 = \dfrac{1}{2}\sigma_1\) | \(E_2 = \dfrac{1}{2}E_1\)
- **D.** \(Q_2 = 2Q_1\) | \(\sigma_2 = \dfrac{1}{4}\sigma_1\) | \(E_2 = \dfrac{1}{4}E_1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124680/*