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AP Physics C: E&M
9.2 Electric Potential
9.1 Electric Potential Energy
IntermediateMCQMathematicalConceptual18.2k
A cross-sectional view of a long cylinder and the path of a charged particle. A large circle centered at the origin represents the cylinder of radius \(R\), filled with light gray shading. A horizontal dashed reference line extends from the cylinder's center to the right beyond the circle. Along this horizontal line, three positions are indicated: a radial distance \(r_1\) inside the circle, the cylinder radius \(R\) at the circle boundary, and a radial distance \(r_2\) outside the circle. At position \(r_1\), a small solid black circle represents the particle, labeled \(+q\), with a short horizontal arrow pointing to the right indicating its direction of motion toward \(r_2\). A dimension arrow from the center to the cylinder boundary is labeled \(R\). The region inside the circle is labeled \(+\lambda\). No other labels, lines, text, or axes appear.
Cross-sectional view of the charged cylinder and the radial trajectory of particle \(+q\).
A very long, solid nonconducting cylinder of radius \(R\) has a uniform positive volume charge density and a total linear charge density \(+\lambda\). A particle of mass \(m\) and positive charge \(q\) is released from rest at a radial distance \(r_1\) from the cylinder's central axis, where \(r_1 < R\). The particle travels radially outward under the influence of the electric field to a final radial distance \(r_2\), where \(r_2 > R\). Which of the following expressions correctly sets up the integral for the work \(W\) done on the particle by the electric field during this displacement?

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