An Electron's Motion: Special Relativity in Action

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SUMMARY

The discussion focuses on the motion of an electron moving at 0.5c in the x-direction when it enters a uniform electric field in the y-direction. Participants conclude that the x-component of the electron's velocity must decrease due to the influence of the electric field, despite the acceleration being primarily in the y-direction. The conversation emphasizes the need to consider relativistic effects and energy loss, particularly in the context of radiation emission, although it is suggested that for small accelerations, this can be ignored.

PREREQUISITES
  • Understanding of special relativity concepts, particularly Lorentz transformations.
  • Familiarity with electric fields and their effects on charged particles.
  • Basic knowledge of classical mechanics and motion in two dimensions.
  • Awareness of radiation emission principles in accelerating charges.
NEXT STEPS
  • Study Lorentz transformations in special relativity to understand velocity changes.
  • Explore the effects of electric fields on charged particles, focusing on classical and relativistic scenarios.
  • Investigate the concept of radiation emitted by accelerating charges, particularly in the context of special relativity.
  • Review classical mechanics principles regarding motion in two dimensions to solidify foundational knowledge.
USEFUL FOR

Students of physics, particularly those studying electromagnetism and special relativity, as well as educators seeking to clarify concepts related to the motion of charged particles in electric fields.

unscientific
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Homework Statement



This is from "Special Relativity" by A.P. French. Chapter 1.

"An electron is moving with speed 0.5c in the x direction enters a region of space where there is a uniform electric field in the y direction. Show that the x component of the velocity of the particle must decrease. "


The Attempt at a Solution



1. Is it because there is acceleration in the y-direction, the electron will emit radiation, hence losing energy/mass? But what has this got to do with relativity?
 
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unscientific said:

Homework Statement



This is from "Special Relativity" by A.P. French. Chapter 1.

"An electron is moving with speed 0.5c in the x direction enters a region of space where there is a uniform electric field in the y direction. Show that the x component of the velocity of the particle must decrease. "

The Attempt at a Solution



1. Is it because there is acceleration in the y-direction, the electron will emit radiation, hence losing energy/mass? But what has this got to do with relativity?
I don't think that's what the author is getting at. Suppose the acceleration is small enough so that you can ignore energy lost via radiation.

Look at what happens classically.
 


SammyS said:
I don't think that's what the author is getting at. Suppose the acceleration is small enough so that you can ignore energy lost via radiation.

Look at what happens classically.

Well..the acceleration is only in the y-direction so the x-component of the velocity remains unchanged while the vertical velocity is increasing?
 


it's an electric field. Ask yourself this "Is the acceleration always only in the y direction?"
 

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