Lorentz Transform: Justifying Use in Acceleration

[Glenda]

In a standard problem of an electron released from the negative plate in an E field between 2 parallel plates in which the velocity must be determined why can the Lorentz transformation be used (involving v^2/c^2) when the electron is undergoing acceleration and there is nothing in the transformations concerning acceleration? (I know the E field parallel o the direction of motion is unchanged) How does one justify using these transformations in a system undergoing acceleration?

 

[Ibix]

You can transform to the frame where the electron is instantaneously at rest without worrying about the history of how it comes to have that speed or how long it will remain at that speed. There is such a frame for any speed less than c, so there is always such a frame available. Then you can think about electromagnetic forces in that frame, or whatever you want to do.

Does that answer your question?

 

[Dale]

In a standard problem of an electron released from the negative plate in an E field between 2 parallel plates in which the velocity must be determined why can the Lorentz transformation be used (involving v^2/c^2) when the electron is undergoing acceleration and there is nothing in the transformations concerning acceleration? (I know the E field parallel o the direction of motion is unchanged) How does one justify using these transformations in a system undergoing acceleration?

You can always use the Lorentz transform, but it doesn't always help make a problem easier to solve. In this case, I think that the simplest frame is the rest frame of the capacitor. As you seem to recognize, an accelerating electron will only be at rest momentarily in any inertial frame.

 

[vanhees71]

For an explicit treatment of the motion of charged particles in an external em. field, see

http://th.physik.uni-frankfurt.de/~hees/pf-faq/srt.pdf

 

[Glenda]

Thanks guys.