---
title: "A particle with mass \\(m\\) and positive charge \\(q\\) is launched at time \\(t = 0\\) with an initial velocity \\(\\vec{v}_0 = v_0 \\hat{i}\\) into a region containing uniform, parallel electric and magnetic fields given by \\(\\vec{E} = E \\hat{k}\\) and \\(\\vec{B} = B \\hat{k}\\), where \\(E\\) and \\(B\\) are positive constants. Gravitational effects are negligible. Which of the following correctly describes the projection of the particle’s trajectory onto the \\(xy\\)-plane and its motion along the \\(z\\)-axis for \\(t > 0\\)?"
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url: "https://nerd-notes.com/ubq/118588/"
date_modified: "2026-08-04T08:11:30+00:00"
---

# A particle with mass \(m\) and positive charge \(q\) is launched at time \(t = 0\) with an initial velocity \(\vec{v}_0 = v_0 \hat{i}\) into a region containing uniform, parallel electric and magnetic fields given by \(\vec{E} = E \hat{k}\) and \(\vec{B} = B \hat{k}\), where \(E\) and \(B\) are positive constants. Gravitational effects are negligible. Which of the following correctly describes the projection of the particle’s trajectory onto the \(xy\)-plane and its motion along the \(z\)-axis for \(t > 0\)?

A particle with mass \(m\) and positive charge \(q\) is launched at time \(t = 0\) with an initial velocity \(\vec{v}_0 = v_0 \hat{i}\) into a region containing uniform, parallel electric and magnetic fields given by \(\vec{E} = E \hat{k}\) and \(\vec{B} = B \hat{k}\), where \(E\) and \(B\) are positive constants. Gravitational effects are negligible. Which of the following correctly describes the projection of the particle's trajectory onto the \(xy\)-plane and its motion along the \(z\)-axis for \(t > 0\)?

![A 3D Cartesian coordinate system with x, y, and z axes labeled. A vector arrow labeled E-vector points vertically along the positive z-axis. A second parallel vector arrow labeled B-vector also points vertically along the positive z-axis. At the origin, a small sphere labeled plus q represents a positive charge. An arrow labeled v_0 starts at the sphere and points horizontally along the positive x-axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831090-gpgLMT.jpg)

- **A.** Projection in \(xy\)-plane: Circle with increasing radius | Motion along \(z\)-axis: Constant acceleration
- **B.** Projection in \(xy\)-plane: Circle with constant radius | Motion along \(z\)-axis: Constant acceleration
- **C.** Projection in \(xy\)-plane: Circle with constant radius | Motion along \(z\)-axis: Constant velocity
- **D.** Projection in \(xy\)-plane: Parabolic trajectory | Motion along \(z\)-axis: Constant velocity

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118588/*