---
title: "A small bead of mass \\(m\\) and positive charge \\(+q\\) is constrained to slide without friction along a rigid, horizontal, circular insulating wire of radius \\(R\\). An external electrostatic arrangement produces an electric potential \\(V(\\theta)\\) along the wire as a function of angular position \\(\\theta\\), as shown in the graph. The bead is launched from \\(\\theta = 0\\) with an initial speed \\(v_0\\) in the direction of increasing \\(\\theta\\) and has sufficient kinetic energy to complete multiple revolutions. Which of the following statements correctly describes the bead’s motion or the forces acting on it as it travels from \\(\\theta = 0\\) to \\(\\theta = 2\\pi\\)?"
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url: "https://nerd-notes.com/ubq/124509/"
date_modified: "2026-09-28T14:08:25+00:00"
---

# A small bead of mass \(m\) and positive charge \(+q\) is constrained to slide without friction along a rigid, horizontal, circular insulating wire of radius \(R\). An external electrostatic arrangement produces an electric potential \(V(\theta)\) along the wire as a function of angular position \(\theta\), as shown in the graph. The bead is launched from \(\theta = 0\) with an initial speed \(v_0\) in the direction of increasing \(\theta\) and has sufficient kinetic energy to complete multiple revolutions. Which of the following statements correctly describes the bead’s motion or the forces acting on it as it travels from \(\theta = 0\) to \(\theta = 2\pi\)?

A small bead of mass \(m\) and positive charge \(+q\) is constrained to slide without friction along a rigid, horizontal, circular insulating wire of radius \(R\). An external electrostatic arrangement produces an electric potential \(V(\theta)\) along the wire as a function of angular position \(\theta\), as shown in the graph. The bead is launched from \(\theta = 0\) with an initial speed \(v_0\) in the direction of increasing \(\theta\) and has sufficient kinetic energy to complete multiple revolutions. Which of the following statements correctly describes the bead's motion or the forces acting on it as it travels from \(\theta = 0\) to \(\theta = 2\pi\)?

![A Cartesian coordinate plot showing electric potential as a function of angle. The horizontal axis is labeled \theta\text{ (rad)} and has five tick marks labeled 0, \pi/2, \pi, 3\pi/2, and 2\pi. The vertical axis is labeled V\text{ (V)} and has three tick marks labeled 10, 30, and 50. A single solid curve begins at (0, 30), rises smoothly with decreasing slope to a horizontal tangent at a crest at (\pi/2, 50), curves downward through an inflection point at (\pi, 30), reaches a horizontal tangent at a trough at (3\pi/2, 10), and rises smoothly to an inflection point at (2\pi, 30). Thin dashed horizontal and vertical projection lines connect each of the two extrema to their respective coordinate values on both axes. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604504-5nPeGA.jpg)

- **A.** At \(\theta = \dfrac{\pi}{2}\), the bead experiences its maximum tangential acceleration because the electric potential has its maximum value.
- **B.** Between \(\theta = \dfrac{\pi}{2}\) and \(\theta = \dfrac{3\pi}{2}\), the normal force exerted by the wire does positive work on the bead to increase its kinetic energy.
- **C.** At \(\theta = \pi\), the tangential acceleration of the bead is directed opposite to its velocity because the slope of the potential graph is negative.
- **D.** At \(\theta = \pi\), the bead has its maximum tangential acceleration in the direction of motion, and at \(\theta = \dfrac{3\pi}{2}\), the bead attains its maximum speed.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124509/*