What is the Magnetic Field of Coaxial Cable?

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

The diagram shows a coaxial cable to give us a better understanding of the interior. The electrical connections are also shown, (one end to source of emf and other to the load).Charge flows out of the source, through the inner conductor, and returns in the outer conductor to the source

Concept

Coaxial cable is a type of cable with an inner conductor enclosed by an insulating layer and conductive shielding. Most have an insulating outer jacket as well. The illustration described depicts the general construction of a cable. The middle conductor carries an electrical pulse.The key to the coaxial cable's success has been its shielded design, which allows the cable's copper core to transmit data quickly, and is not susceptible to environmental damage.

Let's now calculate the self-inductance of the coaxial cable shown in Figure 1. The connections are made as shown. The current flows through the circuit loop of the cable. This current induces an opposite emf which opposes the change in current. The magnetic field (B) for a long straight wire at a distance r is :

$B=\frac{{\mu }_{0}I}{2\pi r}$

and that the magnetic field lines are circles centred on the wire. Integration is performed to get the total magnetic flux. Consider an area element (dA) whose length equals the length (l) and whose width (dr) is measured radially outward from the conductor (Figure 2). The magnetic field is normal to the area. Therefore, the number of magnetic lines threading the area element is concentric with the inner conductor. We consider a small area, i.e. a small strip from the conductor, dA = l dr. So we replace the area element as BdA = Bl dr. We determine the total flux by integrating Bl. dr from the radially from the axias to the outer).

$\begin{array}{c}d\phi =Bda\\ =Bldr\end{array}$

Substituting for B, we have

$d\varphi =\frac{\mu Ildr}{2\pi r}$

Hence, the total flux threading the conducting loop is

$\begin{array}{c}\varphi =\int d\varphi \\ =\frac{{\mu }_{o}Il}{2\pi }{\int }_{r1}^{r2}\frac{dr}{r}\\ =\frac{{\mu }_{o}Il}{2\pi }\mathrm{ln}\left(\frac{r2}{r1}\right)\end{array}$

The self-inductance is flux per unit length

$\begin{array}{c}L=\frac{\varphi }{I}\\ =\frac{{\mu }_{o}}{2\pi }\mathrm{ln}\left(\frac{r2}{r1}\right)\end{array}$

Thus we get the self-inductance of the coaxial cable is only dependant on the permeability of the material and the cable geometry.

Categories of Coaxial Cables

The shielded architecture of coaxial cables has been critical to their performance, allowing the cable's copper core to relay data easily while avoiding interference or disruption from environmental factors.RG-6, RG-11, and RG-59 are the three most popular cable sizes; RG is an abbreviation for radio guide. The numbers on the different RG cable variations correspond to the diameter (59 meaning .059, and 6 meaning .06, etc.). They are often referred to as RF cables, which stand for radio frequency.Coaxial cables are categorized into three types as per radio government (RG) ratings −

• RG – 59: Impedance:75W (cable TV)
• RG – 58: Impedance:50W (thin Ethernet)
• RG – 11: Impedance:50W (thick Ethernet)

Signal Leakage

Signal leaking is the passage of electromagnetic fields through some kind ofcable's barrier in all directions. Ingress is the passing of an outside signal through a wire, which can cause noise and distortion of the target signal. The movement of a signal meant to stay inside the cable into the outer world is known as egress, and it can result in a weakened signal at the end of the cable as well as radio frequency interference to neighbouring equipment.

A better shield will consist of a perfect conductor with no cracks, openings, or bumps attached to a perfect ground. A smooth solid highly conductive shield, on the other hand, would be thick, inflexible, and costly. This form of coax is used for direct feeds to commercial radio transmission towers.

Skin Effect on cables: The amplitude of an alternating current in a conductor deteriorates exponentially with depth under the surface, with penetration depth equal to the square root of the resistivity. Which implies that, even in a shield of finite thickness, any current can always travel on the opposing surface of the conductor.For a complete conductor, all current flows at the surface, with no entry towards or through the conductor. Real cables have a shield made of an incomplete, but normally very fine, conductor, so any leakage is unavoidable.

Applications of Coaxial Cables

• In analog telephone networks: About 10,000 voice signals can be transmitted through single coaxial cable..
• In digital telephone networks: It has a good data transmission rate (600 Mbps).
• In MANs
• The layers of conductors reduce interference of signals thus permitting greater cable lengths for transmission.
• Television signals, radio signal, short length signals (from signal generators)  are transmitted through these cables.
• In LAN connection, computers are connected through these cables and also widely used in cable broadband.

• The wide frequency range is ideal for multiple television broadcasts.
• The wide bandwidth of these cables permits HD (high definition) video transmission.

Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

• Bachelors in Science (Physics)
• Masters in Science (Physics)
• Bachelors in Engineering (Mechanical)

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