Calculating Self-Inductance in Coaxial Cables

In summary, the conversation discusses the calculation of self inductance per unit length of a coaxial cable with concentric cylindrical conductors. The inner conductor has radius a, while the outer conductor has inner radius b and outer radius d. The equation for inductance between two conducting plates is used, but there is a question about the effect of the outer conductor's inner and outer radius. The assumption that (b-a) >> a and (b-a) >> (d-b) is necessary for applying Ampere's law in order to draw an amperian loop between the inner and outer conductors.
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Homework Statement



A coaxial cable is made from concentric cylindrical conductors. The radius of the inner conductor is a and the outer comductor has inner radius b and outer radius d. Calculate the self inductance per unit length of the cable. You may assume that (b-a) >> a and (b-a) >> (d-b). Why is this assumption necessary.


Homework Equations





The Attempt at a Solution



Ok so i know that if we take the conducting plates to be think i can work out the inductance to be u0/2pi ln(b/a)

But what difference does it make that the outer one has an inner and outer radius? How do i work it out now?

Also why is the assumption necessary?
 
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  • #2
Can Ampere's law always be applied without regard for what is outside the amperian loop?

So in this case, in the space between the inner cable and outer cable can i just draw an amperian loop and apply ampere's law? If so - why do i need to assume (b-a) >> a and (b-a) >> (d-b)?

Thanks
 
  • #3
anyone?
 
  • #4
should i post this in advanced phys?
 
  • #5


As a scientist, it is important to understand the underlying principles and assumptions behind any calculation. In this case, the assumption that (b-a) >> a and (b-a) >> (d-b) is necessary because it ensures that the inner conductor is significantly smaller than the outer conductor. This allows us to simplify the calculation and assume that the magnetic field lines are confined within the inner conductor, as the outer conductor essentially acts as a shield. If this assumption was not made, the calculation would become much more complex and may not accurately reflect the true self-inductance of the coaxial cable. Therefore, it is necessary to make this assumption in order to accurately calculate the self-inductance per unit length of the cable.
 

Related to Calculating Self-Inductance in Coaxial Cables

1. What is self-inductance in a coaxial cable?

Self-inductance is a property of a circuit that describes the ability of the circuit to generate an opposing voltage when the current in the circuit changes. In a coaxial cable, self-inductance refers to the ability of the cable to store energy in the form of a magnetic field when an electric current is flowing through it.

2. How is self-inductance calculated in a coaxial cable?

The self-inductance of a coaxial cable can be calculated using the following formula: L = (μ/8π) * ln(b/a), where L is the self-inductance in henries, μ is the permeability of the medium between the inner and outer conductors, b is the outer radius of the cable, and a is the inner radius of the cable.

3. What factors affect the self-inductance of a coaxial cable?

The self-inductance of a coaxial cable is affected by several factors, including the geometry of the cable (such as the distance between the inner and outer conductors), the material used for the conductors, and the presence of any surrounding materials or nearby conductors that could affect the magnetic field.

4. Why is self-inductance important in coaxial cables?

Self-inductance is important in coaxial cables because it can cause interference and affect the performance of the cable. When the current in a coaxial cable changes, the self-inductance can cause a voltage drop, which can lead to signal loss and distortion. Therefore, it is important to calculate and minimize the self-inductance in order to maintain the integrity of the signal.

5. How can the self-inductance of a coaxial cable be reduced?

The self-inductance of a coaxial cable can be reduced by using materials with higher permeability for the inner and outer conductors, decreasing the distance between the conductors, and minimizing the presence of any nearby conductors or materials that could affect the magnetic field. Additionally, using a braided shield or adding ferrite beads along the cable can also help reduce self-inductance.

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