Quasi-static Approximation for coaxial wires

In summary, the conversation discusses a coaxial cable with voltage sources at one end and a short circuit at the other. The question is asked about the dominant field in DC conditions. It is determined that in the previous question with current sources, the magnetic field is dominant. However, in this situation, it is stated that the electric field is dominant. The conversation also raises concerns about the feasibility of the situation and the ambiguity of the term "dominant."
  • #1
StasKO
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Homework Statement



A coaxial cable with inner radius a and outer radius b lies on the z-axis (such that the cable's axis merges with the z-axis). its length (along z-axis) is L. at z=-L there are voltage sources that are distributed uniformly connecting the inner wire to the outer one. at z=0 there is a short circuit. all conductors are perfect.

what is the dominant field?

Homework Equations



the dominant field is the one that exists in DC conditions

The Attempt at a Solution



Im totally stuck. in a previos question instead of the voltage sources there were current sources so that was easy - at DC only current flows so the magnetic field is the dominant. I think that since there is a short circuit and all conductors are perfect than changing the source does not change anything since current still flows in DC and the magnetic field is the dominant but in the solution it says that its the electric field that is dominant.

thanks!
 
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  • #2
"voltage sources at z = -L"? How can you have more gthan one source at one point?

Anyway, the situation is impossible in the steady state since the cable, being a perfect conducror and shorted at the z=0 end, would result in infinite current.

However, if you assume the voltage is appplied as a step at t=0 and L is long enough, then the current is limited to the characteristic impedance of the cable until the return voltage hits the source, or T = 2L/v with v the velocity of propagation.

Ayway, I think the question of what is "dominant" is extremely imprecise.
 

FAQ: Quasi-static Approximation for coaxial wires

1. What is the Quasi-static Approximation for coaxial wires?

The Quasi-static Approximation for coaxial wires is a mathematical model used to simplify the analysis of electromagnetic fields in coaxial cables. It assumes that the electric and magnetic fields inside the cable are constant or slowly varying, and neglects the effects of time-varying fields and wave propagation.

2. Why is the Quasi-static Approximation used for coaxial wires?

The Quasi-static Approximation is used for coaxial wires because it greatly simplifies the calculations involved in analyzing the electromagnetic fields. This is especially useful for practical applications where the cable dimensions are small compared to the wavelength of the signals being transmitted, making the assumption of a slowly varying field valid.

3. What are the limitations of the Quasi-static Approximation for coaxial wires?

The Quasi-static Approximation is not suitable for high-frequency applications, as it neglects the effects of wave propagation and assumes a constant or slowly varying field. It also does not account for skin effect, where the current tends to flow on the surface of the conductor rather than through its entire cross-section.

4. How is the Quasi-static Approximation for coaxial wires calculated?

The Quasi-static Approximation is calculated using Maxwell's equations, specifically the equations for electrostatics and magnetostatics. These equations are solved for the electric and magnetic fields, assuming a slowly varying or constant field, and taking into account the boundary conditions at the interface between the two conductors of the coaxial cable.

5. What are the practical applications of the Quasi-static Approximation for coaxial wires?

The Quasi-static Approximation is commonly used in the design and analysis of coaxial cables for various applications, such as in telecommunications, RF and microwave systems, and medical devices. It is also used in the development of transmission line models for simulating the behavior of coaxial cables in electronic circuits.

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