Solve Cyclotron Motion Homework

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SUMMARY

The discussion centers on solving a cyclotron motion problem involving an electron accelerated through a 10 kV potential difference in a magnetic field. The participant calculated the radius of the electron's path to be 10.669 cm using the relationship mv²/R = qvB, but arrived at an incorrect magnetic field strength of B = 4.1 * 10^-7 T. The angle theta, which is crucial for accurate calculations, was confirmed to be 15°, highlighting the importance of geometric considerations in such problems.

PREREQUISITES
  • Understanding of cyclotron motion and Lorentz force
  • Familiarity with the principles of electric potential and kinetic energy conversion
  • Knowledge of magnetic fields and their effects on charged particles
  • Basic geometry for calculating angles and distances in circular motion
NEXT STEPS
  • Review the derivation of the cyclotron frequency and its applications
  • Study the effects of varying magnetic field strengths on particle trajectories
  • Explore the relationship between potential difference and kinetic energy in charged particles
  • Learn about the use of vector components in analyzing forces in circular motion
USEFUL FOR

Physics students, educators, and anyone involved in electromagnetism or particle motion analysis will benefit from this discussion.

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Homework Statement


An electron in a cathode-ray tube is accelerated through a potential difference of 10 kV, then passes through the d = 2.4-cm-wide region of uniform magnetic field in the figure.
33.P59.jpg


Homework Equations


- Am I taking the entirely wrong approach in the solution?

The Attempt at a Solution


Since this is circular motion, we can draw a circle which intersects the square in the picture at where the electron exits the cathode ray tubes and the place it exits the square. Geometry then gives the angle between the tangent to the latter point and the hypotenuse, and we find that the radius is 10.669 cm. We could then use mv^2/R = qvB, and we know that 1/2mv^2 = q*10000 from the cathode ray tube. Solving for B gives B = 4.1 * 10^-7 T, which is incorrect.
 

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What is the angle theta?
It's not given in your question, how did you calculate the radius?
 
I didn't realize it wasn't given in the figure. Theta is 15°.
 

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