https://changzh.me/en/tags/magnetic-field/Recent content in Magnetic Field on Blog of BrianHugoenThu, 16 Jul 2026 11:50:00 +0800https://changzh.me/en/posts/bounded-field-gravity-particle/Thu, 16 Jul 2026 11:50:00 +0800https://changzh.me/en/posts/bounded-field-gravity-particle/<p>A classic high-school physics problem: a charged particle enters a bounded uniform magnetic field perpendicularly, and we ask how strong the field must be so the particle &ldquo;just exits through the right boundary.&rdquo; The standard solution ignores gravity, and the trajectory is a clean circular arc. But what happens if <strong>gravity is included and the problem is flipped — the field is given, and the width is what we seek</strong>? The answer is: the circle becomes a <strong>cycloid</strong>, and the problem can still be solved elegantly — in two quite different ways. This post documents that extended problem (B6 Extension) and its two solutions.</p>