# Surface Charges on a Coaxial Cable

• cpburris
In summary, To find ##\sigma_b## and ##\sigma_c##, a Gaussian surface of a cylinder of length ##L## and radius ##c>r>b## can be used. Using Gauss' Law, the electric field is found to be zero inside the outer conductor, resulting in the equation $$0=2 \pi L\left(b\sigma_b+a\sigma\right)$$. The value for ##\sigma_b## can be easily solved using this equation. However, for ##\sigma_c##, there is no given information about the total charge on the outer cylinder or the coaxial cable as a whole. This leads to the possibility that ##\sigma_c## is arbitrary, unless it is assumed that the outer conductor
cpburris
Gold Member
Homework Statement
A long coaxial cable consists of a conducting inner cylinder of radius ##a## and a thick outer conducting cylinder of inner radius ##b## and outer radius ##c## (Note: ##a<b<c##). The surface charge density on the inner cylinder is ##\sigma##. Find the surface charge densities ##\sigma_b## & ##\sigma_c##.
Relevant Equations
##E_{inside conductor}=0##
Gauss' Law - ##\oint \vec E \cdot d \vec A = \frac {Q_{enclosed}} {\epsilon_0}##
To find ##\sigma_b## I can use a Gaussian surface of a cylinder of length ##L## and radius ##c>r>b##. Since that is inside of the outer conductor, I know the electric field is zero, so I have from Gauss' Law, $$0=2 \pi L\left(b\sigma_b+a\sigma\right)$$ and easily solve for ##\sigma_b##. For ##\sigma_c## however, I am unsure how to proceed. The problem does not give any information about the total charge on the outer cylinder or the coaxial cable as a whole, and it would seem to me that without knowing one of these ##\sigma_c## is arbitrary. Is there something I am missing or is there an issue with the statement of the problem?

Strictly speaking there is the issue that the total charge on the outer conductor is not specified as you correctly pointed out. I think that in this case you may safely assume that the outer conductor bears no net charge.

## 1. What is a surface charge on a coaxial cable?

A surface charge on a coaxial cable refers to the accumulation of electric charge on the outer surface of the cable, caused by the flow of current through the cable.

## 2. How does a surface charge affect the performance of a coaxial cable?

A surface charge can distort the electric field inside the cable, leading to signal loss and interference. It can also cause voltage breakdown and damage to the cable.

## 3. What causes a surface charge to build up on a coaxial cable?

A surface charge can build up due to various factors such as the mismatch of impedance, presence of contaminants or moisture on the cable, or inadequate shielding.

## 4. How can a surface charge be reduced on a coaxial cable?

A surface charge can be reduced by using proper grounding and shielding techniques, ensuring the cable is free of contaminants, and using a cable with the correct impedance for the application.

## 5. Are there any safety concerns associated with surface charges on coaxial cables?

Yes, a high surface charge can lead to voltage breakdown and pose a safety hazard. It is important to properly ground and shield coaxial cables to prevent any potential safety risks.

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