---
title: "In Configuration 1, two point particles with charges \\(+q\\) and \\(-q\\) are initially held at rest at a separation distance \\(r_0\\). In Configuration 2, two point particles with charges \\(+q\\) and \\(+q\\) are initially held at rest at the same separation distance \\(r_0\\). An external agent slowly increases the separation between the particles in each configuration from \\(r_0\\) to \\(3r_0\\) such that the kinetic energy of the particles remains zero throughout the process. Which of the following correctly compares the work \\(W_1\\) done by the external agent in Configuration 1 to the work \\(W_2\\) done by the external agent in Configuration 2, and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/121047/"
date_modified: "2026-08-23T04:57:35+00:00"
---

# In Configuration 1, two point particles with charges \(+q\) and \(-q\) are initially held at rest at a separation distance \(r_0\). In Configuration 2, two point particles with charges \(+q\) and \(+q\) are initially held at rest at the same separation distance \(r_0\). An external agent slowly increases the separation between the particles in each configuration from \(r_0\) to \(3r_0\) such that the kinetic energy of the particles remains zero throughout the process. Which of the following correctly compares the work \(W_1\) done by the external agent in Configuration 1 to the work \(W_2\) done by the external agent in Configuration 2, and provides the correct justification?

In Configuration 1, two point particles with charges \(+q\) and \(-q\) are initially held at rest at a separation distance \(r_0\). In Configuration 2, two point particles with charges \(+q\) and \(+q\) are initially held at rest at the same separation distance \(r_0\). An external agent slowly increases the separation between the particles in each configuration from \(r_0\) to \(3r_0\) such that the kinetic energy of the particles remains zero throughout the process. Which of the following correctly compares the work \(W_1\) done by the external agent in Configuration 1 to the work \(W_2\) done by the external agent in Configuration 2, and provides the correct justification?

![Two horizontal panels arranged vertically. The upper panel labeled Configuration 1 shows two circular particles separated horizontally by a distance labeled \(r_0\); the left particle is labeled \(+q\) and the right particle is labeled \(-q\). The lower panel labeled Configuration 2 shows two identical circular particles separated horizontally by the same distance \(r_0\); the left particle is labeled \(+q\) and the right particle is labeled \(+q\). A horizontal double-headed dimension arrow indicates the separation \(r_0\) between particle centers in each panel. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461055-PdPvkt.jpg)

- **A.** \(W_1 > 0\) and \(W_2 < 0\), because the external agent must apply a force in the direction of displacement to overcome the attractive electrostatic force in Configuration 1, whereas the external agent applies a force opposite the displacement to restrain the repulsive electrostatic force in Configuration 2.
- **B.** \(W_1 < 0\) and \(W_2 > 0\), because the conservative electric field does positive work when separating opposite charges and negative work when separating like charges.
- **C.** \(W_1 > 0\) and \(W_2 > 0\), because moving charges farther apart always increases the stored electric potential energy regardless of the sign of the interacting charges.
- **D.** \(W_1 < 0\) and \(W_2 < 0\), because the magnitude of the electrostatic force decreases as separation increases in both configurations, which causes a net decrease in potential energy.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121047/*