An electron is launched between two plates

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SUMMARY

An electron launched between two parallel, neutral, conducting plates must achieve a minimum speed to avoid collision with the plates. The relationship governing this scenario is derived from the equations F = BIL and F = ma, leading to the conclusion that the minimum speed v is given by v = (BqL/m)ln(t). Additionally, to prevent deflection, an electric field must be established between the plates, which requires determining the polarity of the plates once charged. The discussion emphasizes the importance of understanding the trajectory of an electron in a magnetic field, which is typically circular.

PREREQUISITES
  • Understanding of classical mechanics, specifically Newton's second law (F = ma).
  • Familiarity with electromagnetic theory, particularly the Lorentz force law (F = evB).
  • Knowledge of calculus, especially integration techniques.
  • Basic principles of electric fields and their effects on charged particles.
NEXT STEPS
  • Explore the concept of the Lorentz force in greater detail.
  • Study the behavior of charged particles in magnetic fields, focusing on circular motion.
  • Learn about electric fields and their role in particle deflection.
  • Investigate the relationship between electric and magnetic fields in electromagnetic theory.
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Students in physics, particularly those studying electromagnetism and mechanics, as well as educators seeking to enhance their understanding of particle dynamics in electric and magnetic fields.

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Homework Statement


An electron is launched between two parallel, neutral, conducting plates that are each L long and separated by a distance d with a uniform magnetic field of magnitude B permeated between them.

(a) What is the minimum speed the particle must have to traverse the region without striking either plate?

(b) What electric field prevents the electron from deflecting? Indicate the polarity of the plates (once charged) if they are to provide this field.

Homework Equations


[/B]
F = BIL

F = ma

The Attempt at a Solution


[/B]
So what i did was set the equations equal to each other to get BIL = ma then I turned a into dv/dt and turn I into q/t getting me BqL/t = mdv/dt I then rearrange the equation so look like BLq/mt dt = dv I then took the integral of both sides and got v = (BqL/m)ln(t) the problem is I don't how to get d into the equation and I don't think t should be in the answer.
 
Last edited:
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Hi, mmm strange combination of formulas ... , the force of an electron ##e## that moves with a velocity ##v## in a magnetic field ##B## is ##F=evB##...
 
A second hint: think if the trajectory of an electron in a magnetic field will be linear or circular ?
 

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