# Need help finding the electric fields in a coaxial cable with charged conductors

• physicsidiot1
In summary, the problem involves a coaxial cable with a long solid inner conductor and a thin outer conductor with a line charge density of +lambda and a uniformly distributed charge of -lambda, respectively. The electric field can be found using Gaussian cylindrical symmetry for the inner and outer conductor, but for the space between the conductors, a cylindrical closed "container" must be defined and Gauss' law applied. The electric field outside the cable can also be found using Gaussian surfaces.
physicsidiot1

## Homework Statement

A coaxial cable consists of a long solid inner cylindrical conductor, radius a, and a thin outer cylindrical conductor of average radius b>a. Suppose the inner conductor has a line charge density of +lambda while the outer conductor has a uniformly distributed charge of -lambda. Find the electric field (as a function of r) in a) inside the inner conductor, b) between conductors and c) the outside cable

## Homework Equations

E=q/Epsilon0 E=q/(4piEpsilonr^2)

## The Attempt at a Solution

I would imagine using Gaussian cylindrical symmetry could help find the field for the inside and outside cable. However, I cannot figure out how to find the field between the conductors. A full explanation of this problem would be so greatly appreciated, as I am struggling to grasp the effect of oppositely charged conductors in electric fields. Thanks.

You must define a cylindrical closed "container" for the inner conductor's charge at radius r between a and b and apply Gauss' law. If you make the cylinder infinitely long you can ignore what happens at the ends.

Hello physicsidiot1,

Welcome to Physics Forums!

a) Remember, the inner conductor is a conductor. That little fact turns out to be quite important.

b) Consider a cylindrical Gaussian surface, with radius r, such that a < r < b (and the Gaussian surface and the cable share the same axis). Given the symmetry, the Gaussian surface vector is always parallel to the electric field lines (except for the end-caps which are perpendicular).

What is the surface area of the Gaussian surface (ignoring end-caps)? What is the charge enclosed within the Gaussian surface?

What does Gauss' law have to say about that?

c) Do you mean the electric field outside the cable (as opposed to "the outside cable")?

## 1. What is a coaxial cable?

A coaxial cable is a type of transmission line that is used to transfer signals and power between two points. It consists of two conductors, an inner conductor surrounded by an outer conductor, separated by an insulating material.

## 2. How are the conductors in a coaxial cable charged?

The inner and outer conductors in a coaxial cable are typically charged by connecting them to a power source, such as a battery or a power supply. The charge on the conductors is what creates the electric field within the cable.

## 3. How do I calculate the electric field in a coaxial cable?

The electric field in a coaxial cable can be calculated using the formula E = V/d, where E is the electric field strength, V is the potential difference between the conductors, and d is the distance between the conductors.

## 4. Does the electric field in a coaxial cable change along its length?

Yes, the electric field in a coaxial cable changes along its length. It is strongest near the charged conductors and decreases as you move away from them.

## 5. What factors can affect the electric field in a coaxial cable?

The electric field in a coaxial cable can be affected by factors such as the charge on the conductors, the distance between the conductors, and the insulating material between them. It can also be affected by external factors such as the presence of other charged objects nearby.

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