Doubts on Ampère's Law and Coaxial Cables

In summary, the conversation discusses a doubt about Ampère's law and its application to a coaxial cable with equal and opposed currents in the core and shield. It is mentioned that the magnetic field outside the outer conductor is zero due to the summation of currents in a loop around the cable. However, it is difficult to visualize this in points close to the outer conductor. The conversation also raises the question of whether there would be a field in the region between the center and the shield if there is no current in the core conductor, to which the answer is no.
  • #1
xareu
25
6
I have a doubt about Ampère's that keeps me awake at night haha, but I think that for a more knowledgeable person it may seem pretty obvious. I've seen in several books that, in a coaxial cable with equal and opposed currents in the core and shield, the magnetic field outside the outer conductor is zero, after using Ampères Law (the summation of the currents in a loop around the whole cable, with opposite currents, is 0, assuming that in this particular arrangement H and dl have the same direction). Leaving apart the calculation, for me it's difficult to visualize it in the points which lay very close to the outer conductor. How can the field be zero there?
In the same cable, but with no current in the core conductor, only in the screen, is there field in the region from the centre to the shield?
 
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  • #2
xareu said:
In the same cable, but with no current in the core conductor, only in the screen, is there field in the region from the centre to the shield?
No, the field would be 0 in that region.
 

1. What is Ampère's Law and how does it relate to coaxial cables?

Ampère's Law is a fundamental law in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through that loop. In the case of coaxial cables, Ampère's Law is used to calculate the magnetic field around the outer conductor of the cable, which is important for understanding the behavior of the cable in different situations.

2. Are there any limitations to using Ampère's Law for analyzing coaxial cables?

Yes, there are some limitations to using Ampère's Law for analyzing coaxial cables. This law assumes that the conductors are infinitely long, straight, and have a uniform current distribution. In reality, coaxial cables may have bends, discontinuities, and non-uniform current distribution, which can affect the accuracy of the calculations.

3. How does the geometry of a coaxial cable affect the application of Ampère's Law?

The geometry of a coaxial cable can affect the application of Ampère's Law in several ways. For example, the distance between the inner and outer conductors can affect the strength of the magnetic field, and the presence of any obstructions or non-uniformity in the conductor can also impact the accuracy of the calculations.

4. Can Ampère's Law be used to calculate the magnetic field inside a coaxial cable?

No, Ampère's Law cannot be used to calculate the magnetic field inside a coaxial cable. This law only applies to the magnetic field outside of a closed loop, and the magnetic field inside a coaxial cable is not a closed loop. To calculate the magnetic field inside a coaxial cable, other methods, such as the Biot-Savart Law, must be used.

5. How can doubts about Ampère's Law and coaxial cables be resolved?

Doubts about Ampère's Law and coaxial cables can be resolved through further research and experimentation. Scientists can conduct experiments to measure the magnetic field around coaxial cables and compare the results to the predictions of Ampère's Law. If there are discrepancies, this can lead to further investigations and improvements in our understanding of the behavior of coaxial cables.

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