Electrostatics -- the case of a charged cylinder

[Pablo3]

Hello , I post a message because I will need help with this exercise I would like to knowif my answer are
good,

I'm french :

An infinite hollow cylinder charge is constituted of a sheath whose outer limits are R2 and R3. Wearing a uniform charge density ρ

Question 2)calculate the total electric field E at any point M ( r ,θ, z) into space.
3) Give the appearance of E according to the relevant variable .
4 ) Calculate the electrostatic energy carried by a cylinder length L.
And my answers are:
2)There are 3 cases:
The first r<R2
Whe can say that :

And Er(r)=0 because ρ=0.
Second and third case:

3)

I had a problem to place A and B because I do not know how far they must be put to the origin O ( 0,0,0) .
I do not know either the distance required between R2 and R3 on the drawing or the shape of the curve.
4)

and Ep=0 because ρ=0.

Also the beginning of my reasoning is here(in french,but the only the formulas are important).

 

[TSny]

In all three cases, you have not correctly calculated the charge enclosed in the Gaussian surface.

In the region where r < R₂, what is the charge density?

For each of the other two cases, make sure you draw a picture showing your Gaussian surface.

 

[Pablo3]

the load is 0 because there is no load , I wrote it above.
And the other cases it's "rho" no?

 

[TSny]

the load is 0 because there is no load , I wrote it above.

OK, I overlooked that. So, your answer for r < R₂ is correct.

And the other cases it's "rho" no?

For the second and third parts, make sure you are taking into account that ρ = 0 for the hollow region.
Also, for the second part where R₂ < r < R₃, make sure you are finding the charge enclosed in your Gaussian surface. Thus, make sure you can draw and describe the dimensions of your Gaussian surface.

 

[Pablo3]

Ah okay!

I had not taken it into account between R2 and R3 actually , thank you very much.
Hum for r>R3 it's 0,and for R2<r<R3 it varies between 0 and rho I think.
I will think carefully before you answer in this case!