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title: "A particle with charge \\(q = +2.0 \\text{ } \\mu\\text{C}\\) is constrained to move along the \\(x\\)-axis in a region of electric potential \\(V(x)\\), as shown in the graph. The graph features a local potential minimum of \\(V = 10 \\text{ V}\\) at \\(x = 2.0 \\text{ cm}\\), bounded by a potential peak of \\(V = 50 \\text{ V}\\) at \\(x = 0.0 \\text{ cm}\\) to the left and a potential peak of \\(V = 40 \\text{ V}\\) at \\(x = 5.0 \\text{ cm}\\) to the right. What is the maximum kinetic energy the particle can have at \\(x = 2.0 \\text{ cm}\\) such that it remains bound within the potential well near \\(x = 2.0 \\text{ cm}\\)?"
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url: "https://nerd-notes.com/ubq/118110/"
date_modified: "2026-08-04T08:05:10+00:00"
---

# A particle with charge \(q = +2.0 \text{ } \mu\text{C}\) is constrained to move along the \(x\)-axis in a region of electric potential \(V(x)\), as shown in the graph. The graph features a local potential minimum of \(V = 10 \text{ V}\) at \(x = 2.0 \text{ cm}\), bounded by a potential peak of \(V = 50 \text{ V}\) at \(x = 0.0 \text{ cm}\) to the left and a potential peak of \(V = 40 \text{ V}\) at \(x = 5.0 \text{ cm}\) to the right. What is the maximum kinetic energy the particle can have at \(x = 2.0 \text{ cm}\) such that it remains bound within the potential well near \(x = 2.0 \text{ cm}\)?

A particle with charge \(q = +2.0 \text{ } \mu\text{C}\) is constrained to move along the \(x\)-axis in a region of electric potential \(V(x)\), as shown in the graph. The graph features a local potential minimum of \(V = 10 \text{ V}\) at \(x = 2.0 \text{ cm}\), bounded by a potential peak of \(V = 50 \text{ V}\) at \(x = 0.0 \text{ cm}\) to the left and a potential peak of \(V = 40 \text{ V}\) at \(x = 5.0 \text{ cm}\) to the right. What is the maximum kinetic energy the particle can have at \(x = 2.0 \text{ cm}\) such that it remains bound within the potential well near \(x = 2.0 \text{ cm}\)?

![A 2D Cartesian plot showing electric potential \(V\) in volts on the vertical axis versus position \(x\) in centimeters on the horizontal axis. The vertical axis ranges from 0 to 60 with major tick marks labeled 0, 10, 20, 30, 40, 50, 60. The horizontal axis ranges from 0 to 8 with major tick marks labeled 0, 1, 2, 3, 4, 5, 6, 7, 8. A single continuous smooth curve starts at \((0, 50)\), slopes downward to a local minimum at \((2, 10)\), rises upward to a local peak at \((5, 40)\), and then decays downward toward \((8, 0)\). Dashed horizontal grid lines extend from the vertical axis to key points on the curve: one at \(V = 10\text{ V}\) extending to \((2, 10)\), one at \(V = 40\text{ V}\) extending to \((5, 40)\), and one at \(V = 50\text{ V}\) extending to \((0, 50)\). Dashed vertical grid lines extend from the horizontal axis to key points: one at \(x = 2\text{ cm}\) up to \((2, 10)\) and one at \(x = 5\text{ cm}\) up to \((5, 40)\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830710-tsn4kU.jpg)

- **A.** \(20 \text{ } \mu\text{J}\)
- **B.** \(40 \text{ } \mu\text{J}\)
- **C.** \(60 \text{ } \mu\text{J}\)
- **D.** \(80 \text{ } \mu\text{J}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118110/*