Motion of Charged Particles in Field Uniform B-field E=0

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The discussion focuses on understanding the motion of charged particles in a uniform magnetic field where the electric field is zero. The user seeks to determine the perpendicular velocity of the particles without relying on the Larmor radius or angular frequency. They express confusion about how to apply vector operations like cross and dot products in this context, especially without known angles. The user is engaged in a science research project and is eager to learn more about the relevant math and physics concepts despite a tight schedule. The conversation emphasizes the theoretical approach to particle motion in magnetic fields.
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Hello!

So I've been working on proving to myself different parts of https://ocw.mit.edu/courses/nuclear...a-physics-i-fall-2003/lecture-notes/chap2.pdf packet for several weeks.

Under 2.1 Uniform B field, E=0, for the Larmor Radius, I need to know perpendicular v, but I want to figure it out in terms of anything except rL and omega.

I'm especially wondering what "perpendicular velocity" would mean and how to find it. I was thinking about cross products and dot products, but what would I cross with the velocity? I also don't know any angles, because right now I have no data- I'm just trying to do theoretical and trying to avoid angles.

It's late at night, thank you for helping me!
 
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Hi! I also wanted to say that I'm in AP Calculus right now, and in Physics C AP. This is for my science research project, so I'm willing to put in the time and effort to learn math/physics that I don't know yet, although I am in a really big time crunch.
 

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