What is the Physics behind the Coaxial Cable?

In summary, a coaxial cable consists of an inner wire and a concentric cylindrical outer conductor. By applying Gauss's Law and using symmetry, it can be shown that there is no net charge on the outside of the outer conductor, as the positive charge on the inner surface of the outer conductor cancels out the negative charge on the wire, resulting in a net charge of 0 on the outer surface. This is due to the fact that there is no electric field inside a conductor in electrostatic equilibrium, and the equal charges on the inner and outer conductor create a neutral charge distribution inside the outer conductor.
  • #1
Bryan52803
8
0

Homework Statement


"A coaxial cable consists of an inner wire and a concentric cylindrical outer conductor. If the conductors carry equal but opposite charges, show that there is no net charge on the outside of the outer conductor.


Homework Equations


Gauss's Law


The Attempt at a Solution


I tried to approach this problem as logically as possible before laying any numbers to paper or manipulating equations, but was not able to even get that far. Our teacher brushed over very quickly the concept of uniform volume charge distribution and conductors in electric fields. I know there can be no electric field within a conductor. Therefore, if we assume the wire carries a negative charge, then that means there is an excess of electrons that will move themselves to the surface of the conductor, correct? ("If a conductor in electrostatic equilibrium carries a net charge, it must reside on the conductor surface"). So we have a negative field resulting in the cavity thus far. However, if we assume the outside cylindrical shell to be positive in charge, then there will be a positive net charge on the surface of the shell, both on the inside by the wire and the outside as well, correct? Now because of uniform charge distribution, the charge on the inside of the shell will in effect cancel its own field out, still leaving a negative field inside the cavity, but how is the net charge on the outside of the shell in any way negated by the wire? It has to have a positive net charge according to Gauss's law? Thanks for any tips, suggestions or hints!

-Confused student
 
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  • #2
Hint... looking at the outer conductor... what is the field inside that conductor... what is the field outside of that conductor... uses gauss' law and symmetry for this part...

Then finally... when you know the field inside and outside the conductor... do gauss law using a tiny volume that cross the outer boundary of this conductor...
 
  • #3
Bryan52803 said:
So we have a negative field resulting in the cavity thus far. However, if we assume the outside cylindrical shell to be positive in charge, then there will be a positive net charge on the surface of the shell, both on the inside by the wire and the outside as well, correct?

No... you're right about the inside, but not the outside.
 
  • #4
learningphysics said:
Hint... looking at the outer conductor... what is the field inside that conductor... what is the field outside of that conductor... uses gauss' law and symmetry for this part...

Then finally... when you know the field inside and outside the conductor... do gauss law using a tiny volume that cross the outer boundary of this conductor...

Thanks for the speedy reply!

Actually INSIDE the material, there is no field. In the cavity of the outer conductor, there is a negative field resulting from the wire, E = k(-q)/r^2, r being the distance from the wire and -q being the charge on the wire. If the outer conductor has a charge of +q, then the total enclosed charge by a gaussian surface surrounding the entire cable would be 0, meaning there can be no field outside of the cable, and if there's no field outside the cable, there can be no net charge on the outer surface?

If that is the logic, then what is going on in terms of electron arrangement and such to make this occur? I think I get it, but it's still a little hazy and I want to make sure I fully understand the concept.
 
  • #5
Actually here's another way to think about it... actually simpler this way... since the inner and outer conductor have equal charges... and since the field inside the outer conductor is 0... that means the net charge inside a gaussian surface within the outer conductor is 0... That means that all the positive charge must be on the inner surface... hence the outer surface must have a net charge of 0, and by symmetry a charge density of 0...
 
  • #6
I understand! Thanks for the explanation!
 
  • #7
Bryan52803 said:
I understand! Thanks for the explanation!

You're welcome. :smile:
 

1. What is a coaxial cable?

A coaxial cable is a type of electrical cable that has two conductors: a center wire surrounded by a tubular insulating layer, which is then encased in a metallic shield and outer jacket. This design allows for high-frequency signals to be transmitted with minimal interference.

2. What is the physics behind the transmission of signals through a coaxial cable?

The transmission of signals through a coaxial cable is based on the principles of electromagnetism. When an electrical signal is applied to the center conductor, it creates an electromagnetic field that induces a current in the surrounding metallic shield. This current, in turn, creates another electromagnetic field that travels through the cable and allows for the transmission of the signal.

3. What factors affect the performance of a coaxial cable?

The performance of a coaxial cable can be affected by various factors, including the quality of the materials used, the thickness of the conductors and insulating layers, the frequency of the signal being transmitted, and the length of the cable. Any damage or interference to the cable can also impact its performance.

4. How does the design of a coaxial cable prevent signal loss?

The design of a coaxial cable is specifically engineered to minimize signal loss. The insulating layer between the center conductor and the metallic shield helps to reduce interference, and the shield itself serves as a barrier to prevent external signals from entering the cable. Additionally, the cable's uniform impedance helps to maintain signal strength over long distances.

5. What are some common applications of coaxial cables?

Coaxial cables are widely used in various industries, including telecommunications, television and radio broadcasting, and computer networking. They are commonly used to transmit high-frequency signals, such as cable television, internet, and telephone signals. They are also used in medical equipment, military communication systems, and scientific instruments.

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