Coaxial Cable/charge density

In summary, The problem involves a long coaxial cable with an inner cylinder of radius "a" and a outer coaxial cylinder with inner radius "b" and outer radius "c". The outer cylinder has no net charge and is mounted on insulating supports. The inner cylinder has a positive charge per unit length λ. The electric field is calculated at any point between the cylinders a distance "r" from the axis to be (2kλ)/r, and outside the outer cylinder to be (-2kλ)/r. The charge per unit length on the inner surface of the outer cylinder is equal and opposite to λ, while the outer surface has no charge. This is determined using Gauss's law.
  • #1
critter
9
0
1. A long coaxial cable consists of an inner cylindrical conductor with radius "a" and an outer coaxial cylinder with inner radius "b" and outer radius "c." The outer cylinder is mounded on insulating supports and has no net charge. The inner cylinder has a positive charge per unit length λ. Calculate the electric field (A) at any point between the cylinders a distance "r" from the axis and (B) at any point outside the outer cylinder. (C) Find the charge per unit length on the inner surface and on the outer surface of the outer cylinder.



2. Parts A and B seem really simple, but maybe I'm looking at this wrong. I don't understand how the outer cylinder has any charge density since it was already stated that the outer cylinder has no net charge.



3. I think A and B might have the same answer: (2kλ)/r. This equation was given in the chapter summary in my textbook, but I somehow think they might be wanting a more extensive proof. I have no idea how to approach C since the information given in the problem seems contradictory.
 
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  • #2
critter said:
I don't understand how the outer cylinder has any charge density since it was already stated that the outer cylinder has no net charge.
Just because the net charge is zero doesn't mean the surface charge densities are zero.
 
  • #3
How would I solve for the density with what I'm given? Would they both be equal to λ?
 
  • #4
critter said:
How would I solve for the density with what I'm given?
Use Gauss's law.
Would they both be equal to λ?
In magnitude.
 
  • #5
I think I'm starting to understand. There is some charge q enclosed between the two cylinders. The inner cylinder produces the electric field E=(2kλ)/r, and the total flux is equal to 0, so the outer cylinder must produce a field E=(-2kλ)/r. In that way, the magnitudes of the densities would be the same. Am I thinking about this correctly?
 
  • #6
critter said:
I think I'm starting to understand. There is some charge q enclosed between the two cylinders. The inner cylinder produces the electric field E=(2kλ)/r, and the total flux is equal to 0, so the outer cylinder must produce a field E=(-2kλ)/r. In that way, the magnitudes of the densities would be the same. Am I thinking about this correctly?
I'm not exactly sure what you are referring to when you say outer cylinder, since it has two surfaces. (I think you have it, but are expressing it unclearly.)

The inner cylinder (radius a) produces a field E=(2kλ)/r for r > a.

Since the field within the outer conducting cylinder (b < r < c) must be zero, Gauss's law tells you that the total charge enclosed must be zero. Thus the inner surface of the outer shell (at r = b) must have a charge equal and opposite to λ.
 

1. What is a coaxial cable?

A coaxial cable is a type of electrical cable that has two concentric conductors, an inner conductor surrounded by an outer conductor. The two conductors are separated by a dielectric material and the cable is then covered by an insulating layer.

2. How does a coaxial cable work?

A coaxial cable works by carrying electrical signals from one point to another. The inner conductor carries the signal while the outer conductor acts as a shield to protect the signal from outside interference. The dielectric material between the two conductors helps to maintain the integrity of the signal by preventing it from leaking out.

3. What is charge density in a coaxial cable?

Charge density in a coaxial cable refers to the amount of charge per unit length that is present on the inner and outer conductors. This charge density is responsible for creating an electric field within the cable, which allows the signal to be transmitted from one end to the other.

4. How is charge density calculated in a coaxial cable?

Charge density in a coaxial cable can be calculated by dividing the total charge on either the inner or outer conductor by the length of the cable. This will give the charge per unit length for that particular conductor.

5. What factors can affect charge density in a coaxial cable?

There are several factors that can affect charge density in a coaxial cable. These include the material and thickness of the conductors, the dielectric material used, and the distance between the two conductors. Additionally, the voltage and current being transmitted through the cable can also affect the charge density.

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