---
title: "Two widely separated conducting spheres, Sphere 1 of radius \\(R\\) and Sphere 2 of radius \\(2R\\), are located in a vacuum. Sphere 1 initially carries a net charge \\(Q_0\\) and has electrostatic potential energy \\(U_0\\), while Sphere 2 is initially uncharged. The two spheres are then connected by a thin conducting wire and the system is allowed to reach electrostatic equilibrium. Which of the following statements correctly describes what happens to the total electrostatic potential energy of the two-sphere system and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/124520/"
date_modified: "2026-09-28T14:08:30+00:00"
---

# Two widely separated conducting spheres, Sphere 1 of radius \(R\) and Sphere 2 of radius \(2R\), are located in a vacuum. Sphere 1 initially carries a net charge \(Q_0\) and has electrostatic potential energy \(U_0\), while Sphere 2 is initially uncharged. The two spheres are then connected by a thin conducting wire and the system is allowed to reach electrostatic equilibrium. Which of the following statements correctly describes what happens to the total electrostatic potential energy of the two-sphere system and provides the correct physical justification?

Two widely separated conducting spheres, Sphere 1 of radius \(R\) and Sphere 2 of radius \(2R\), are located in a vacuum. Sphere 1 initially carries a net charge \(Q_0\) and has electrostatic potential energy \(U_0\), while Sphere 2 is initially uncharged. The two spheres are then connected by a thin conducting wire and the system is allowed to reach electrostatic equilibrium. Which of the following statements correctly describes what happens to the total electrostatic potential energy of the two-sphere system and provides the correct physical justification?

![Two shaded gray circles representing spheres are positioned side by side along a horizontal line against a white background. The left circle has a radius labeled \(R\) indicated by a horizontal arrow from its center to its right edge, and is labeled Sphere 1. The right circle is twice as wide as the left circle, with a radius labeled \(2R\) indicated by a horizontal arrow from its center to its right edge, and is labeled Sphere 2. A single thin horizontal line connects the top edge of Sphere 1 to the top edge of Sphere 2, representing a connecting wire. Above Sphere 1, text indicates initial charge \(Q_0\). Above Sphere 2, text indicates initial charge 0. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604510-58e2K2.jpg)

- **A.** The total electrostatic energy remains the same because the system is electrically isolated and electric charge is conserved.
- **B.** The total electrostatic energy decreases because transient current through the wire dissipates \(\dfrac{1}{3}U_0\) as thermal energy until each sphere carries an equal charge of \(\dfrac{1}{2}Q_0\).
- **C.** The total electrostatic energy decreases because transient current through the wire dissipates \(\dfrac{2}{3}U_0\) as thermal energy until both spheres reach the same electric potential.
- **D.** The total electrostatic energy remains the same because the electrostatic force is conservative and no work is done on the system by an external agent.

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