---
title: "A charged particle of mass \\(m\\) and charge \\(+q\\) enters a region containing a static, non-uniform magnetic field with an initial velocity directed entirely along the \\(+x\\)-axis. Due to the magnetic forces exerted by the field, the particle is deflected such that its velocity component in the \\(x\\)-direction, \\(v_x\\), smoothly decreases to zero at time \\(t_0\\) and reverses direction, exiting the magnetic field region at time \\(2t_0\\). Which of the following graphs best represents the particle’s total kinetic energy \\(K_{\\text{total}}\\) (solid line) and its \\(x\\)-component kinetic energy \\(K_x = \\dfrac{1}{2}mv_x^2\\) (dashed line) as functions of time \\(t\\) from \\(t = 0\\) to \\(t = 2t_0\\)?"
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url: "https://nerd-notes.com/ubq/123384/"
date_modified: "2026-09-28T11:58:19+00:00"
---

# A charged particle of mass \(m\) and charge \(+q\) enters a region containing a static, non-uniform magnetic field with an initial velocity directed entirely along the \(+x\)-axis. Due to the magnetic forces exerted by the field, the particle is deflected such that its velocity component in the \(x\)-direction, \(v_x\), smoothly decreases to zero at time \(t_0\) and reverses direction, exiting the magnetic field region at time \(2t_0\). Which of the following graphs best represents the particle’s total kinetic energy \(K_{\text{total}}\) (solid line) and its \(x\)-component kinetic energy \(K_x = \dfrac{1}{2}mv_x^2\) (dashed line) as functions of time \(t\) from \(t = 0\) to \(t = 2t_0\)?

A charged particle of mass \(m\) and charge \(+q\) enters a region containing a static, non-uniform magnetic field with an initial velocity directed entirely along the \(+x\)-axis. Due to the magnetic forces exerted by the field, the particle is deflected such that its velocity component in the \(x\)-direction, \(v_x\), smoothly decreases to zero at time \(t_0\) and reverses direction, exiting the magnetic field region at time \(2t_0\). Which of the following graphs best represents the particle's total kinetic energy \(K_{\text{total}}\) (solid line) and its \(x\)-component kinetic energy \(K_x = \dfrac{1}{2}mv_x^2\) (dashed line) as functions of time \(t\) from \(t = 0\) to \(t = 2t_0\)?

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123384/*