An Electron's Motion: Special Relativity in Action

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Homework Help Overview

The problem involves an electron moving at a speed of 0.5c in the x direction, entering a uniform electric field in the y direction. The task is to demonstrate that the x component of the electron's velocity must decrease, which relates to concepts in special relativity.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the implications of acceleration in the y-direction and its potential effects on the x component of velocity. Questions arise about the relationship between radiation emission and relativistic effects, as well as classical interpretations of the motion.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some suggest considering classical mechanics while questioning the assumptions about energy loss due to radiation. There is no explicit consensus yet, but various lines of reasoning are being examined.

Contextual Notes

Participants note the need to consider the effects of the electric field and the nature of acceleration in different directions. There is an emphasis on understanding the classical versus relativistic perspectives without resolving the underlying assumptions.

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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