Electric Field of Coaxial Cable

In summary, the logarithmic part of the integral is equal to ln c/a, and the c^2 and ab terms come from taking the antiderivative and using the property of logarithms mentioned above.
  • #1
Lavace
62
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http://img154.imageshack.us/img154/165/integrallll.jpg

After working it out myself, I have the logarithim part equal to:

[ln b - lna] + [ln c - ln b] = [ln b/a + ln c/b] = ln c/a (Not sure about this statement!)

I don't understand where the c^2 and ab came from with this integral?

Any help?

Thanks!
 
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  • #2
Lavace said:
After working it out myself, I have the logarithim part equal to:

[ln b - lna] + [ln c - ln b] = [ln b/a + ln c/b] = ln c/a (Not sure about this statement!)

I don't understand where the c^2 and ab came from with this integral?

Any help?

Thanks!

Take a careful look at the factors in front of each logarithm (they are different by a factor of 2) and remember that [itex]p\ln(x)=\ln(x^p)[/itex]
 

1. What is an electric field of a coaxial cable?

The electric field of a coaxial cable is a vector field that describes the strength and direction of the electric force at any point surrounding the cable. It is created by the movement of electric charges within the cable and is responsible for transmitting electrical signals.

2. How is the electric field of a coaxial cable calculated?

The electric field of a coaxial cable can be calculated using the equation E = (1/2πε) * (Q/r), where E is the electric field strength, ε is the permittivity of the surrounding medium, Q is the charge on the inner conductor, and r is the distance from the center of the cable.

3. What factors affect the electric field of a coaxial cable?

The electric field of a coaxial cable is affected by several factors, including the distance between the inner and outer conductors, the diameter of the conductors, and the type of dielectric material between the conductors. Additionally, the presence of any external electric fields can also influence the overall electric field of the cable.

4. How does the electric field of a coaxial cable differ from other types of cables?

The electric field of a coaxial cable differs from other types of cables, such as parallel or twisted pair cables, in that it is contained within the cable itself. This allows for better transmission of signals and less interference from external sources. Additionally, the electric field within a coaxial cable is more uniform and concentrated compared to other cable types.

5. What are some practical applications of the electric field of a coaxial cable?

The electric field of a coaxial cable is utilized in many practical applications, including telecommunications, cable television, and computer networking. It is also commonly used in scientific and medical equipment, such as MRI machines, as well as in industrial and military equipment for communication purposes.

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