What is the radius of a charged ion in a magnetic field?

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SUMMARY

The discussion focuses on calculating the radius of a singly charged positive ion with a mass of 2.50 x 10-26 kg, accelerated through a potential difference of 250 V, as it enters a magnetic field of 0.500 T. The participant attempted to derive the radius using the equations of motion in magnetic fields, specifically setting the magnetic force equal to the centripetal force. The key equations referenced include Bqv = mv2/r, which relates the magnetic field, charge, velocity, and radius of the ion's path.

PREREQUISITES
  • Understanding of magnetic fields and forces
  • Familiarity with the concepts of electric potential and energy conservation
  • Knowledge of centripetal motion and its equations
  • Basic algebra and manipulation of equations
NEXT STEPS
  • Study the derivation of the radius of charged particles in magnetic fields using Bqv = mv2/r
  • Learn about energy conservation principles in charged particle motion
  • Explore the relationship between electric fields and potential difference (V = ED)
  • Investigate the effects of varying magnetic field strengths on particle trajectories
USEFUL FOR

Students studying physics, particularly those focusing on electromagnetism and charged particle dynamics, as well as educators looking for practical examples of magnetic field interactions with ions.

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Homework Statement


A singly charged positive ion has a mass of 2.50 x 10^-26kg. After being accelerated through a potential difference of 250 V, the ion enters a magnetic field of 0.500 T, in a direction perpendicular to the field.

Homework Equations


Calculate the radius of the path of the ion in the field.

The Attempt at a Solution


Firstly, I drew this picture to try to help me with the problem:
http://img411.imageshack.us/img411/4197/picxc7.jpg

I've tried to set Fm = Fe, therefore coming up with the derived equation of V=E/B, but I don't know E.

I then tried to find the electric field by using the voltage, but I don't know the distance. (V=ED)

I also tried setting Fm = Fc, getting Bqv = mv^2/r, and finally resulting in Bqr/v=m. I had B, q, and m, but I didn't have r and v.

Thanks for reading.
 
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Try energy conservation
 
turdferguson said:
Try energy conservation

You're a lifesaver.
 

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