Maximum speed of an electron in an ideal solenoid

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SUMMARY

The maximum speed of an electron in an ideal solenoid with 1200 turns/m, a radius of 10 cm, and a current of 4.0 A is calculated to be 5.3 × 107 m/s. The magnetic field (B) is determined using the formula B = μ₀nI, resulting in a value of 0.006032 T. The radius of curvature for the electron's trajectory is critical for this calculation, as it must not exceed the solenoid's radius to avoid collision with its sides. The relationship between the electron's speed (v), mass (m), charge (q), and magnetic field (B) is expressed through the equation r = (mv)/(qB).

PREREQUISITES
  • Understanding of electromagnetic theory, specifically solenoids
  • Familiarity with the Lorentz force and circular motion
  • Knowledge of fundamental physics equations involving magnetic fields
  • Basic calculus for solving equations involving variables
NEXT STEPS
  • Study the derivation of the magnetic field in solenoids using Ampère's Law
  • Learn about the motion of charged particles in magnetic fields
  • Explore the concept of radius of curvature in circular motion
  • Investigate the effects of varying current and turns per meter on magnetic field strength
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Homework Statement



A particular ideal solenoid has 1200 turns/m, a radius of 10 cm, and a current of 4.0 A. An electron is fired from the axis of the solenoid in a direction perpendicular to the axis. What is the maximum speed the electron can have if it is not run into the side of the solenoid?


I know the answer is 5.3 ×10^7 m/s but I have no idea how to arrive there... Any help would be great. Thanks.


Homework Equations



u=4pi*10^-7 T m/A

n=N/L

B=u*n*I

The Attempt at a Solution



I just plugged in the values to get B which ended up being .006032T and than used r=(mv)/(qB) to get v... but that didn't seem to work.
 
Physics news on Phys.org
Don't confuse the radius of the solenoid with the radius of curvature of the electron's trajectory. The electron's trajectory will describe a circle. What's its maximum diameter?
 

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