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title: "A particle with positive charge \\(q\\) moves at a constant speed in a circular orbit of radius \\(r_0\\) around a fixed central particle with positive charge \\(+Q\\). Which of the following correctly states the net work done by the electric field on the particle of charge \\(q\\) during one complete orbit and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/118089/"
date_modified: "2026-08-04T08:05:03+00:00"
---

# A particle with positive charge \(q\) moves at a constant speed in a circular orbit of radius \(r_0\) around a fixed central particle with positive charge \(+Q\). Which of the following correctly states the net work done by the electric field on the particle of charge \(q\) during one complete orbit and provides the correct physical justification?

A particle with positive charge \(q\) moves at a constant speed in a circular orbit of radius \(r_0\) around a fixed central particle with positive charge \(+Q\). Which of the following correctly states the net work done by the electric field on the particle of charge \(q\) during one complete orbit and provides the correct physical justification?

![A central fixed point charge labeled +Q is at the origin. A dashed circular orbit of radius r_0 surrounds +Q. A small positive charge labeled +q is positioned on the right side of the orbit. A velocity vector arrow labeled v points vertically upward tangent to the circle. An electric force vector arrow labeled F_E points horizontally to the right along the radial line away from +Q. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830703-ckfD85.jpg)

- **A.** Net work: \(\dfrac{1}{4\pi\varepsilon_0}\dfrac{Qq}{r_0}\) | Justification: The charge completes one full orbit at a constant distance \(r_0\) from the central charge.
- **B.** Net work: \(0\) | Justification: The electric force is perpendicular to the particle's displacement vector at every point along the circular path.
- **C.** Net work: \(0\) | Justification: The electric force acts parallel to the particle's direction of motion around the circular path.
- **D.** Net work: \(\dfrac{1}{4\pi\varepsilon_0}\dfrac{2\pi Qq}{r_0}\) | Justification: The magnitude of the electric force is constant and acts along the entire circular path of length \(2\pi r_0\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118089/*