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title: "Two particles with equal mass \\(m\\) and equal charge magnitude \\(q\\), one positively charged (\\(+q\\)) and one negatively charged (\\(-q\\)), are launched with the same speed \\(v_0\\) into a region containing a uniform magnetic field \\(\\vec{B}\\) directed perpendicular to their initial velocity vectors. Both particles follow circular paths within the magnetic field. Which of the following correctly compares the work \\(W_+\\) done by the magnetic field on the positive charge to the work \\(W_-\\) done on the negative charge after each particle completes one full revolution, and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/116366/"
date_modified: "2026-08-03T12:23:37+00:00"
---

# Two particles with equal mass \(m\) and equal charge magnitude \(q\), one positively charged (\(+q\)) and one negatively charged (\(-q\)), are launched with the same speed \(v_0\) into a region containing a uniform magnetic field \(\vec{B}\) directed perpendicular to their initial velocity vectors. Both particles follow circular paths within the magnetic field. Which of the following correctly compares the work \(W_+\) done by the magnetic field on the positive charge to the work \(W_-\) done on the negative charge after each particle completes one full revolution, and provides the correct justification?

Two particles with equal mass \(m\) and equal charge magnitude \(q\), one positively charged (\(+q\)) and one negatively charged (\(-q\)), are launched with the same speed \(v_0\) into a region containing a uniform magnetic field \(\vec{B}\) directed perpendicular to their initial velocity vectors. Both particles follow circular paths within the magnetic field. Which of the following correctly compares the work \(W_+\) done by the magnetic field on the positive charge to the work \(W_-\) done on the negative charge after each particle completes one full revolution, and provides the correct justification?

![A schematic diagram showing a uniform magnetic field perpendicular to the page, represented by a grid of small x symbols labeled B. Two charged particles enter the region from the bottom traveling vertically upward with speed v_0. On the left, a positive particle labeled +q moves along a counterclockwise circular trajectory of radius R. On the right, a negative particle labeled -q moves along a clockwise circular trajectory of radius R. At two points along each circular path, a velocity arrow v is drawn tangent to the curve, and a magnetic force arrow F_B is drawn pointing directly toward the center of the circle, perpendicular to the velocity arrow. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785759817-K0wQpd.jpg)

- **A.** \(W_+ > W_-\) because the magnetic force acts along the direction of motion for the positive charge and opposite to the direction of motion for the negative charge.
- **B.** \(W_+ < W_-\) because the magnetic force acts opposite to the direction of motion for the positive charge and along the direction of motion for the negative charge.
- **C.** \(W_+ = W_- = 0\) because the magnetic force on each charge is perpendicular to its velocity vector at every point along the path.
- **D.** \(W_+ = W_- = 2\pi q v_0 B R\) because both particles experience a centripetal force of magnitude \(q v_0 B\) over a distance equal to the circumference \(2\pi R\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116366/*