Charged Particles Moving in Electromagnetic Fields

In this video I show that space curves can be used to model charged particle motion in orthogonally oriented electric and magnetic fields. Depending on the speed and position of a charged particle, the motion is either a cycloid or a trochoid (a more general version of a cycloid). I then take a detour into the mainstream physics of charged particle motion in electromagnetic fields in general, and read up on magnetic mirrors, null lines, Earth's magnetic field lines, Van Allen Belts, and the Northern Lights. Buckle up!

#math #3D #spacecurves #GeoGebra #calculator

Timestamps

• Charged particle in orthogonally oriented electric and magnetic fields: 0:00
  • Particle moves either in a cycloid or trochoid curve: 2:00
  • Cycloid traces point on a circle, trochoid is more general point above, on, or below a circle: 3:00
  • Enclosing 3D curve in a tube makes it more visible: 4:18
  • Graphing trochoid in GeoGebra: https://www.geogebra.org/calculator/rmhpa57e 5:16
  • I used Surface command vis Grok AI: https://x.com/i/grok/share/IX3lwQmHjrdNfPlW7x4T9qU1V 7:35
• Physics of Charges particles in Electromagnetic Fields: 11:45
  • Charged particle motion simulator via Java applet extension: 14:00
• Single particle motion in Electric and Magnetic Fields UCLA experiments: 15:05
• Mirror magnetic field or magnetic mirror: https://en.wikipedia.org/wiki/Magnetic_mirror 27:25
• Tutorial 1: Magnetic mirror confinement of electric charges towards weak magnetic field lines: 29:13
  • Torus magnetic mirror confine plasma in nuclear reactors.
  • Van Allen belts are trapped charged particles via magnetic fields.
• Tutorial 2: Basics of magnetic mirror and nuclear reactor plasma trapping: 31:23
  • Charges leak in a toroidal tokomak nuclear reactor towards the less compact magnetic field lines on the outside.
• Back to the UCLA experiments: Replicating charged particle motion in the Earth's ionosphere: 33:33
  • Electromagnetic null line is where EMF strength is zero: https://www.researchgate.net/figure/An-example-of-magnetic-configuration-with-a-null-field-line-magnetic-neutral-loop_fig1_230928661 34:34
• GeoGebra charged particle in Magnetic Field simulator: https://www.geogebra.org/m/qajRP2O4 36:23
• Moving charged particle experiences a Lorentz force from a magnetic field via the right hand rule: 37:46
  • Northern lights are trapped particles: 39:48
• Comparing positive and negative charged particle motion in EMF and Gravity: 41:40
  • Is gravity just a gradient magnetic field? 45:08

Notes and playlists

• Summary: @mes/re-leothreads-wuxwwzrw
• Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GwdMY-E9_4LsmYmO-IxcoX
• Notes: @mes/omhbcxkw
• Vector Functions playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HQl7xTQBS_O8Te8PcpNm4U .

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