# Charge on a rod of infinite length

1.
Charge is distributed through an infinitely long cylinder of radius R in such a way that the charge density is proportional to the distance from the central axis: ß = A r, where A is a constant and ß is the density.
(a) Calculate the total charge contained in a segment of the cylinder of length L.
(b) Calculate the electric field for points outside the cylinder.
(c) Calculate the electric field for points inside the cylinder.

2. Homework Equations :

E=kQ/r charge desity=charge/ length f=kq1q2/r^2

3. So far, I am a bit thrown off by the total charge on A. How can I calculate this without any additional information? I'm not sure if the total charge refers to the electric field around the charge or if it is something else I am not thinking about. I am also unsure of how to go about finding the charge separately for the inside and outside of the rod. Since I am not given a charge for the rod, it only has a specific charge density, I'm not sure how to draw e

haruspex
Homework Helper
Gold Member
if the total charge refers to the electric field
No, it's the charge. Ignore the word "total" in the question, it adds nothing.

in (a) You need to calculate the charge but charge density is not constant, is r dependent, then you must make a volume integration. Cylindrical coordinates are the best for that.
(b) and (c) are a electricity Gauss Theorem problem. Then you need construct the Gauss surface, and remember: only the charge inside the surface is the source of the electric field.