# Charge on a rod of infinite length

In summary, the conversation discusses the distribution of charge through an infinitely long cylinder with a proportional charge density. It also mentions calculating the total charge in a segment of the cylinder, as well as the electric field for points both inside and outside of the cylinder using the equations E=kQ/r, charge density=charge/length, and f=kq1q2/r^2. The best approach for calculating the charge is to use cylindrical coordinates for volume integration, and for the electric field, the Gauss Theorem must be applied, with the understanding that only the charge inside the Gauss surface contributes to the electric field.

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

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.

## 1. What is the concept of charge on a rod of infinite length?

The concept of charge on a rod of infinite length refers to the distribution of electric charge along a hypothetical rod with an infinite length. This charge can either be positive or negative and is typically represented by the letter Q.

## 2. How is the charge on a rod of infinite length calculated?

The charge on a rod of infinite length can be calculated by multiplying the linear charge density (λ) by the length of the rod (L). This can be expressed as Q = λL.

## 3. Can the charge on a rod of infinite length ever be infinite?

No, the charge on a rod of infinite length can never be infinite. This is because the concept of infinite charge is not physically possible and would violate the laws of electromagnetism.

## 4. What is the relationship between charge and electric field on a rod of infinite length?

The charge on a rod of infinite length creates an electric field around it. The strength of this electric field is directly proportional to the charge and inversely proportional to the distance from the rod. This relationship is described by Coulomb's Law.

## 5. How does the charge on a rod of infinite length affect other charged objects?

The charge on a rod of infinite length can interact with other charged objects through electric forces. Depending on the sign of the charges, the objects can either attract or repel each other. The strength of this interaction depends on the magnitude of the charges and the distance between them.