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AP Physics C: E&M
9.3 Conservation of Electric Energy
9.2 Electric Potential
AdvancedMCQMathematicalConceptual12.9k
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.
Electric potential along the circular wire as a function of angular position.
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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