Angles Transversed with Centripetal Acceleration

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SUMMARY

The discussion focuses on calculating the radius of curvature for a proton moving through a uniform magnetic field, specifically addressing the relationship between the exit angle θ and the geometry of the motion. The participant successfully derived the correct answer but challenges the assumption regarding the angle formed by the radii at the entry and exit points. They argue that this angle does not accurately represent the exit velocity's angle relative to the ground, using geometric reasoning to support their claim.

PREREQUISITES
  • Understanding of centripetal acceleration in magnetic fields
  • Knowledge of trigonometric functions, specifically sine
  • Familiarity with the motion of charged particles in magnetic fields
  • Basic geometry related to angles and radii
NEXT STEPS
  • Study the principles of charged particle motion in magnetic fields
  • Learn about the derivation of radius of curvature for charged particles
  • Explore advanced trigonometric applications in physics problems
  • Investigate the effects of varying magnetic field strengths on particle trajectories
USEFUL FOR

Physics students, educators, and anyone interested in the dynamics of charged particles in magnetic fields will benefit from this discussion.

Durin
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Homework Statement


Okay, so the problem is I need to find the radius of curvature for a proton moving through a uniform magnetic field with initial velocity v for some distance d and exiting at angle θ. I was able to get the correct answer; however, I think the apparent assumption made by the person making this problem is wrong.

Homework Equations



sin θ = opposite/hypotenuse.

The Attempt at a Solution



[PLAIN]http://img715.imageshack.us/img715/4710/diagram2.png

This is what I think is wrong.

[PLAIN]http://img194.imageshack.us/img194/6984/diagram1l.png

This is why I think it is wrong.

If my diagrams need to be further explicated, don't hesitate asking.
 
Last edited by a moderator:
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What exactly do you think it's wrong ? State it with words...
What is "h" ? The total length of the path ?
 
h is the height it exits at. It's solved for using the radius. d is the distance it travels along the x-direction.

What I think is wrong is the angle at the top left of the first diagram. According to the correct answer, it appears that the angle the two radii make at the enter and exit points is equal to the angle the exit velocity makes relative to the ground. I used geometry to show why I don't believe that is actually the angle.
 

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