The magnetic field strength required to oscillate an electron

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Discussion Overview

The discussion revolves around the calculation of the magnetic field strength required for an electron to circle along a loop with a specified radius after being accelerated by a potential difference. The scope includes homework-related problem-solving and technical reasoning regarding magnetic fields and forces acting on charged particles.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant calculates the speed of the electron using the equation v = sqrt(2qV/m) and finds it to be approximately 5.93 E5 m/s.
  • The same participant computes the centripetal force and magnetic field strength, concluding B = 3 E4 Tesla.
  • Another participant questions the validity of the equation B = qv/F for field strength, suggesting a need for verification.
  • A later reply emphasizes the importance of carrying units through calculations to ensure correctness and suggests that this practice could help identify errors in the initial calculations.
  • One participant expresses a strong preference for using symbols rather than numerical values until the end of calculations to avoid confusion and errors.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the equations used and the importance of unit consistency in calculations. There is no consensus on the validity of the initial calculations or the appropriateness of the methods employed.

Contextual Notes

Some participants note potential errors in the application of equations and emphasize the necessity of unit analysis, but specific assumptions or definitions that may affect the calculations remain unresolved.

cmcd
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Homework Statement



"An electron is accelerated by a potential difference of 1 V and is injected into vacuum. How strong should the magnetic field in a vacuum be if you want the electron to circle along a loop with a radius of 10^-1m? Please indicate the direction of the magnetic field"




Homework Equations



PE = KE
for speed

F_centripetal =( mv^2) / r
for force

B = qv/F
for field strength




The Attempt at a Solution



v = sqrt(2qV/m)
v= 5.93 E5 m/s

F = 3.2 E-18 Newtons

B = 3 E4 Tesla
 
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Not a textbook question...
 
cmcd said:

Homework Statement



B = qv/F
for field strength

Better check that one.
 
cmcd said:

Homework Statement



"An electron is accelerated by a potential difference of 1 V and is injected into vacuum. How strong should the magnetic field in a vacuum be if you want the electron to circle along a loop with a radius of 10^-1m? Please indicate the direction of the magnetic field"




Homework Equations



PE = KE
for speed

F_centripetal =( mv^2) / r
for force

B = qv/F
for field strength




The Attempt at a Solution



v = sqrt(2qV/m)
v= 5.93 E5 m/s

F = 3.2 E-18 Newtons

B = 3 E4 Tesla

rude man said:
Better check that one.

It is a good practice to carry units along for all quantities in all of your equations. If you had done so, you would have caught this error that rude man is pointing out...
 
I hope you listen to berkeman. There's nothing more important than carrying units along. Then you can check expressions term-by-term for agreement and the correctness of the answer. Which is (one reason) why I oppose using numbers instead of symbols until the very end, and why I abhor labeling e.g. a dependent voltage source as "10I" where I is current and the "10" is meant to be some impedance.
 

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