Charged particle flying into an electric field

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SUMMARY

A proton entering a magnetic field experiences a force described by the equation F = qv × B, where q is the charge, v is the velocity, and B is the magnetic field. The proton's trajectory is helicoidal due to the magnetic force acting perpendicular to its velocity in the x-y plane, resulting in circular motion while maintaining its z-component velocity. The radius of the circular orbit is determined by the charge strength, mass, velocity, and magnetic field strength. This motion occurs because the magnetic force does not act along the direction of the magnetic field.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically Lorentz force law
  • Familiarity with vector mathematics and cross products
  • Knowledge of particle dynamics, including mass and charge interactions
  • Basic concepts of magnetic fields and their representation
NEXT STEPS
  • Study the Lorentz force law in detail, focusing on its applications in particle motion
  • Learn about the properties of magnetic fields and their effects on charged particles
  • Explore the concept of circular motion in electromagnetic fields, including radius calculations
  • Investigate the behavior of other charged particles in magnetic fields, such as electrons and ions
USEFUL FOR

Physics students, educators, and professionals in fields related to electromagnetism and particle physics will benefit from this discussion, particularly those interested in the dynamics of charged particles in magnetic fields.

EdTheHead
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If a proton flies into a magnetic field I've seen the trajectory but I'm not sure about the directions of all the forces involved. In this picture
[PLAIN]http://img7.imageshack.us/img7/7065/helicinbfld.jpg
I drew in a red, blue and yellow arrow. I assume the proton is moving in the direction the red arrow which is along the magnetic field lines but I have no idea what direction it was traveling before it entered the magnetic field. Was it traveling in the direction of the yellow arrow before entering the magnetic field then once it entered got stuck in that helicoidal trajectory because of the force exerted by the magnetic field?

Those green lines I assume are the magnetic field lines. If so why is the proton traveling in their direction?
 
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The magnetic field induces a force on the proton that is equal to
\mathbf{F} = q\mathbf{v}\times\mathbf{B}
Assume that the B field is along the z direction and we can rotate our coordinate system so that the proton has a velocity with only x and z components. Looking only at the force due to the v_x component, you will find that the magnetic field's force causes the charge to move in a circular orbit. This is because the force changes so that it is always normal to the direction of the velocity in the x-y plane (since B is oriented along the z-axis). The radius of this orbit is dependent upon the charge strength, charge's mass, charge's velocity, and the strength of the magnetic field. The force due to the v_z component is zero as this velocity is directed along the direction of the magnetic field. Thus, the result is that the proton moves in a corkscrew motion.
 

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