What is the Magnetic Field Inside a Cylindrical Coaxial Cable?

• Floriane Houenagnon
In summary, a cylindrical coaxial cable is an electrical cable that consists of two cylindrical conductors separated by an insulating material. Its main purpose is to transmit high-frequency signals over long distances with minimal interference. It differs from other types of cables by having a single central conductor surrounded by a cylindrical outer conductor. The advantages of using this type of cable include high bandwidth, low signal loss, and resistance to interference. It is commonly used in telecommunications, cable television, computer networking, and other applications such as medical equipment and military technology.
Floriane Houenagnon
Homework Statement
A portion of along,cylindrical coaxialcable is shown in the accompanying figure. A current I flows down the center conductor, and this current is returned in the outer conductor. Determine the magnetic field in the regions (a) r ≤r1, (b) r2 ≥r ≥r1, (c) r3 ≥r ≥r2, and (d) r ≥r3. Assume that the current is distributed uniformly over the cross sections of the two parts of the cable.
Relevant Equations
B∫dl = μI

Inner current = I1
Outer Current = I2

I = J*A
J = Current Density
A = Area
I have no idea where to start.

The problem is a straightforward application of Ampere's law:

(the magnetic field on the loop) x (loop length) = (permeability) x (total current inside the loop)

Try solving it first for only 1 wire with radius r1 and current I1 for r>r1.

1. What is a cylindrical coaxial cable?

A cylindrical coaxial cable is a type of transmission line used for carrying high-frequency electrical signals. It consists of a central conductor, surrounded by a cylindrical insulating layer, which is then covered by an outer cylindrical conductor. The two conductors are separated by a dielectric material, which helps to reduce signal loss and interference.

2. How does a cylindrical coaxial cable work?

A cylindrical coaxial cable works by carrying electrical signals between two points. The center conductor carries the signal while the outer conductor acts as a shield, minimizing interference from external sources. The dielectric material between the two conductors helps to maintain the signal's strength and quality by preventing them from coming into contact with each other.

3. What are the advantages of using a cylindrical coaxial cable?

There are several advantages to using a cylindrical coaxial cable. It has a higher bandwidth capacity compared to other types of cables, making it suitable for transmitting a wide range of frequencies. It also has a low signal loss and is less susceptible to interference, making it ideal for long-distance transmissions. Additionally, it is relatively easy to install and maintain.

4. What are the applications of cylindrical coaxial cables?

Cylindrical coaxial cables are commonly used in various communication systems, such as cable television, internet connections, and telephone networks. They are also used in radio frequency transmission, military and aerospace systems, medical equipment, and test and measurement devices.

5. Can cylindrical coaxial cables be used for both analog and digital signals?

Yes, cylindrical coaxial cables can be used for both analog and digital signals. They are designed to transmit a wide range of frequencies, making them suitable for carrying both types of signals. However, digital signals may require more advanced and specialized coaxial cables to ensure optimal performance.

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