Surface Charges on a Coaxial Cable

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
  • #1
cpburris
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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?
 
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  • #2
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.
 

Related to Surface Charges on a Coaxial Cable

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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