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Charge on a rod of infinite length

  • #1
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
 

Answers and Replies

  • #2
haruspex
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if the total charge refers to the electric field
No, it's the charge. Ignore the word "total" in the question, it adds nothing.
 
  • #3
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.
 

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