What is the Radius of an Electron Trajectory in a Magnetic Field?

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Homework Help Overview

The problem involves electrons being accelerated through a potential difference and subsequently deflected by a magnetic field. The objective is to determine the radius of the electron's trajectory in the magnetic field.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to relate the kinetic energy gained from the potential difference to the equations governing the motion of the electron in the magnetic field. Some participants question the specifics of the setup, such as the width of the gap through which the electron is accelerated.

Discussion Status

Participants are exploring the relationship between the potential difference and the kinetic energy of the electron. Some guidance has been offered regarding the energy gained by the electron, and there seems to be a progression in understanding as participants discuss the resulting velocity of the electron.

Contextual Notes

The original poster mentions that they are not required to provide a numerical answer, indicating that the problem may be part of a multiple-choice format. There is also a lack of specific information regarding the width of the gap, which some participants have noted.

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Homework Statement



Electrons (mass m, charge –e) are accelerated from rest through a potential difference V and are then deflected by a magnetic field B that is perpendicular to their velocity. Find the radius of the resulting electron trajectory.

Homework Equations


F=\dfrac{mv^2}{r} F=qvB

The Attempt at a Solution



I don't know where to start with this. The electron moves through the potential difference, and presumably gains kinetic energy, but I don't know how to express this in the equations above to get an answer.

Help appreciated.
 
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I am assuming that the e is accelerated through a gap across which there is a potential difference V. What is the width of the gap?
 
grzz said:
I am assuming that the e is accelerated through a gap across which there is a potential difference V. What is the width of the gap?

That's all the info I'm given; I've literally copied and pasted the question.

I'm not being asked to give a numerical answer though. It's a multiple choice question, and this is apparently the answer:

\frac{\sqrt{2mV/e}}{B}
 
The p.d. gives an energy of Ve to the electron.

From this one can find the resulting velocity of the electron.
 
grzz said:
The p.d. gives an energy of Ve to the electron.

From this one can find the resulting velocity of the electron.

Aha! Got it. Thanks for the help :)
 

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