Electric potential of concentr

[fatfatfat]

Electric potential of cylindrical conductor placed in a cylindrical conducting shell

Homework Statement

A cylindrical conducting shell is placed concentric with a cylindrical conductor. Assume that a total charge density λ0 = 2.60 µC/ m is placed on the inner cylinder and a total charge density λ = -2.90 µC/ m is placed on the outer one, r0 = 8.40 cm, r1 = 16.80 cm and r2 = 21.00 cm. Calculate, relative to r = 10·r0 = 84.0 cm:

[1pt] the electric potential at r = 30.80 cm.


Answer: -5.41E+03 V
(I need help figuring out HOW to get this answer, not the answer itself)

Homework Equations

V= the negative inegral of E
λ=Q/2(pi)r

The Attempt at a Solution

So far all I've done is that I've integrated E=2kλ/r and got v=(-2kλ)ln(r)+C for the conducting shell and Vo=(-2kλo)ln(ro)+C for the conductor.

I'm not really sure what to do with the question, though.

I'm thinking I could use those equations to find the potential of both the cylindrical conductor and the cylindrical conducting shell. Then what?

And for the shell, would I have to use the two radiuses to find it on the outside of the shell and the inside too? I have no idea, I need assistance haha.

Help would be appreciated.

 

[Dick]

Gauss' theorem will tell you that the E field depends only on the total charge density contained within the radius. In this case both of your points are outside of the outer shell, so none of the details of the inside matter. You can also do it by just summing the two potentials you have integrated and taking the difference between the two radii.

 

[fatfatfat]

okay, I'll give it a shot, thanks!