An Electron's Motion: Special Relativity in Action

AI Thread Summary
An electron moving at 0.5c in the x direction enters a uniform electric field in the y direction, prompting a discussion on the effects of this field on its motion. The key point is that while the electron experiences acceleration in the y direction, the x component of its velocity must decrease due to relativistic effects. Some participants question the relevance of radiation emission to the problem, suggesting that energy loss can be ignored if the acceleration is small. The conversation emphasizes understanding the classical mechanics involved and the nature of acceleration in different directions. Ultimately, the relationship between electric fields and particle motion under special relativity is central to the discussion.
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?"
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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