---
title: "A particle with mass \\(m\\) and positive charge \\(q\\) is launched into a region of uniform magnetic field \\(\\vec{B} = B_0 \\hat{i}\\) with an initial velocity \\(\\vec{v}_0 = v_x \\hat{i} + v_y \\hat{j}\\), where \\(v_x > 0\\) and \\(v_y > 0\\). Which of the following statements correctly describes the resulting trajectory and the kinetic energy of the particle?"
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url: "https://nerd-notes.com/ubq/123164/"
date_modified: "2026-09-28T11:57:50+00:00"
---

# A particle with mass \(m\) and positive charge \(q\) is launched into a region of uniform magnetic field \(\vec{B} = B_0 \hat{i}\) with an initial velocity \(\vec{v}_0 = v_x \hat{i} + v_y \hat{j}\), where \(v_x > 0\) and \(v_y > 0\). Which of the following statements correctly describes the resulting trajectory and the kinetic energy of the particle?

A particle with mass \(m\) and positive charge \(q\) is launched into a region of uniform magnetic field \(\vec{B} = B_0 \hat{i}\) with an initial velocity \(\vec{v}_0 = v_x \hat{i} + v_y \hat{j}\), where \(v_x > 0\) and \(v_y > 0\). Which of the following statements correctly describes the resulting trajectory and the kinetic energy of the particle?

![A three-dimensional Cartesian coordinate system showing x, y, and z axes with origin labeled O. The x-axis extends horizontally to the right, the y-axis extends vertically upward, and the z-axis extends diagonally forward and to the left. Exactly four parallel horizontal arrows pointing to the right represent a uniform magnetic field labeled \vec{B}. At the origin, a single small circular dot labeled +q represents a positively charged particle. An arrow labeled \vec{v}_0 starts at the origin and points into the first quadrant of the xy-plane at an acute angle to the x-axis, with dashed component segments along the x-axis labeled v_x and along the y-axis labeled v_y. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596670-W6XWQ1.jpg)

- **A.** The particle follows a parabolic path in the \(xy\)-plane with increasing kinetic energy because the perpendicular component of velocity experiences a constant linear acceleration along the magnetic field lines.
- **B.** The particle follows a helical path with increasing pitch along the \(x\)-axis and increasing kinetic energy because the magnetic field continually accelerates the parallel velocity component.
- **C.** The particle follows a helical path with constant pitch along the \(x\)-axis and constant kinetic energy because the magnetic force acts perpendicular to the velocity at all instants, doing zero work.
- **D.** The particle follows a circular path confined to the \(yz\)-plane with constant kinetic energy because the magnetic field exerts an opposing drag force that rapidly reduces the parallel velocity to zero.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123164/*