Electrodynamics homework question

[yakinc]

Hello
I have a question I got which I've been sitting on for weeks.

I have an electron going through a conducting infinite cylinder of R radius. I need to know what the induced charge is on the cylinder, and the potential, for different speeds of the electron. a) for slow speed v<<c b) for fast speed v=c/constant

thanks

 

[Physics Monkey]

Hi yakinc,

Welcome to the forums! There is lots of great help here, but we make you work for it too. So what are your thoughts so far?

 

[Meir Achuz]

Hello
I have a question I got which I've been sitting on for weeks.

I have an electron going through a conducting infinite cylinder of R radius. I need to know what the induced charge is on the cylinder, and the potential, for different speeds of the electron. a) for slow speed v<<c b) for fast speed v=c/constant

thanks

Unless there is something tricky going on, the induced charge would be -q and the potential zero.

 

[Andrew Mason]

Unless there is something tricky going on, the induced charge would be -q and the potential zero.

The tricky thing is with the electron moving at speeds greater than the speed at which electrons can move in the conductor. At such speed, electrons in the conductor may not be not able move quickly enough as the electron moves along the cylinder axis to produce a 0 field everywhere inside the conductor.

AM

 

[yakinc]

I know that if the electron is not moving we always used green's function.
Let's say I take a certain potential on the cylinder, V (which later can be V(t) ) . Then I can easily get the potential as a function of the coordinates. Then I can derive the fields, and from there maybe use the boundry conditions of the fields to have the field inside and out of the cylinder, then to get to the charge distribution (which is what I really need, not just the total charge). but is it similar in electrodynamics? :shy:

 

[pseudovector]

Calculate the fields in a reference frame where the electron is stationary and then apply lorenz transformation for the fields.

 

[yakinc]

that's easy.. why didn't i think of that :)

thanks!