Understanding the Skin Effect: Flux Linkage in a Wire

In summary, the conversation discusses the concept of flux linkage in a wire and how it affects self inductance and impedance. The key detail being questioned is why the flux linked is greatest in the centre of the wire, when the field lines are concentric circles. The conversation suggests looking at a thread on the EE forum for more information and clarification.
  • #1
physiks
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I'm struggling to understand a key detail about this.

My book divides the cross section of a wire into elementary filaments. It then states that the flux linked by the filament in the centre of the wire will be greatest, then this will decrease until at the outermost filaments the only flux linked is from external sources. This would then mean greater self inductance in the middle of the wire, and thus larger impedance so the current flow is greater towards the surface.

Firstly I know flux linkage refers the the magnetic flux crossing an area. Here the field lines in the wire are concentric circles so when dealing with flux linkage we can't be dealing with the linkage through the cross sectional area of the wire as this would be zero. It must be the flux through the cross section of the wire when viewed from above so the field lines penetrate it.

I'm struggling to understand how the flux linked is greatest in the centre. The wire could be thought of as a series of shells, and the B-field due to the wire increases linearly outwards. The field at the centre of the wire is zero. Therefore surely a central elementary filament links zero flux, and the filaments on the outside link the most flux?
 
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  • #2
There is a long thread stickied at the top of the EE forum about this. Maybe have a look at the thread and its related links to see if that helps...
 

1. What is the skin effect?

The skin effect is a phenomenon in which high frequency alternating current (AC) tends to flow near the surface of a conductor, rather than evenly throughout its cross-section. This is due to the resistance of the conductor, which increases as the frequency of the current increases. As a result, the majority of the current flows through the outermost layer of the conductor, known as the "skin".

2. How does the skin effect impact the performance of a wire?

The skin effect increases the effective resistance of a wire, which can lead to energy loss and reduced efficiency in electrical systems. This is particularly important in high frequency applications, such as radio frequency (RF) circuits and power transmission lines.

3. What is flux linkage and how is it related to the skin effect?

Flux linkage is a measure of the amount of magnetic flux that passes through a circuit. In the context of the skin effect, flux linkage is used to describe the amount of flux that is linked to the current flowing through the skin of a conductor. As the skin effect increases the resistance of the wire, it also decreases the flux linkage and can impact the performance of magnetic devices and circuits.

4. How does the skin effect impact the design of electrical systems?

The skin effect must be taken into consideration when designing high frequency electrical systems, as it can affect the performance of wires, cables, and other components. Engineers may need to use specialized materials or techniques to minimize the skin effect and reduce energy loss in these applications.

5. Can the skin effect be used to our advantage in any way?

While the skin effect is generally seen as a hindrance in electrical systems, it can also be utilized to our advantage in certain applications. For example, it can be used to create skin depth gauges for measuring the thickness of conducting materials, or in induction heating processes that rely on the resistance and heating effects of the skin effect.

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