Electron's trajectory in positively charged hollow cylinder

[Mary001]

How an electron moves when it is released from rest to a positively charged hollow cylinder? The hollow cylinder is finite and insulating. The electron is constrained to move only in z direction (into the center of the hollow cylinder). My thinking is that there is no electric field inside the hollow cylinder. Therefore, the electron will not be affected by the electric field. So what causes it to move should be gravitational force and it should travel towards the earth? But an electron's mass is tiny so gravity can be ignored here? Also, the next task asks me to calculate the work done by the electric field on the electron to make it travel. I think I'm not on the right track now.

Any help would be much appreciated.
Thank you.

 

[mfb]

Is this homework?
Edit: moved to homework section now.

My thinking is that there is no electric field inside the hollow cylinder.

There is, as the cylinder is finite.

So what causes it to move should be gravitational force and it should travel towards the earth? But an electron's mass is tiny so gravity can be ignored here?

Gravity can be ignored for electrons. Even the tiniest deviation from some exact geometry of electric fields will be orders of magnitude more important than gravity.

Can you find the electric potential as function of position?

 

[Mary001]

Is this homework?

It is a question from my mid-exam sample

There is, as the cylinder is finite.
Gravity can be ignored for electrons. Even the tiniest deviation from some exact geometry of electric fields will be orders of magnitude more important than gravity.

Oh really? I've read some documents and they say electric field in a hollow cylinder is zero. I can see that in this case, as the finite is finite, there is electric field. But why's that?

Can you find the electric potential as function of position?

Yep, I can. Is it how I should start with to find the work done by the electric field?

 

[mfb]

Oh really? I've read some documents and they say electric field in a hollow cylinder is zero. I can see that in this case, as the finite is finite, there is electric field. But why's that?

Why should it be zero? A value of exactly zero requires something special, like a symmetry (a cylinder of infinite length).

Yep, I can. Is it how I should start with to find the work done by the electric field?

If you can calculate the potential, the work done should be easy.