Skin Depth Confusion: Investigating Different Equations for Paul

In summary, the conversation discusses two different equations for calculating skin depth, one using the angle δ = tan-1(loss tangent) and the other using the skin depth δ directly. The first equation seems to give the same value of 1.57m for all large values of the loss tangent, while the second equation gives the correct result. It is mentioned that the first equation may only be valid for a certain range of loss tangents.
  • #1
paul_harris77
52
0
Dear all

I am slightly confused over the equations for skin depth. My university notes give me the equations:

[tex]\delta = [/tex] tan-1 (tan[tex]\delta[/tex]) = [tex]\frac{\sigma}{\omega \epsilon}[/tex] (loss tangent)

where [tex]\delta[/tex] is skin depth and [tex]\sigma[/tex] is conductivity.

I am also given the equation:

[tex]\delta = [/tex] [tex]\frac{1}{\sqrt{\pi f \mu \sigma}}[/tex]

However, for the situation below, they both yield different skin depths.

f = 1MHz

w = [tex]2\pi f[/tex]

[tex]\sigma = 5.8 \times 10^{7}[/tex] Sm-1

Using the first equation:

[tex]\delta = [/tex] tan-1( [tex]\frac{5.8\times 10^{7}}{2\pi \times 1 \times 10^{6} \times 8.85 \times 10^{-12}} = 1.57m[/tex])

Using the second equation:

[tex]\delta = [/tex] [tex]\frac{1}{\sqrt{\pi \times 1 \times 10^{6} \times 4\pi \times 10^{-7} \times 5.8 \times 10^{7}}} = 66.09\mu m[/tex]

It seems like the first equation gives 1.57 for all large values of the loss tangent, whereas the second equation gives the correct result.

Is the first equation valid for a certain range of loss tangents only?

Any help would be greatly appreciated.

Many thanks

Regards

Paul
 
Engineering news on Phys.org
  • #2
You are using two different definitions for δ.

The angle δ = tan-1(loss tangent) is in radians

The skin depth δ is in length (e.g., mm).

Bob S
 

1. What is skin depth confusion?

Skin depth confusion refers to the confusion that arises when trying to calculate the skin depth of a material using different equations, particularly for the Paul equation. Skin depth is a measure of how far electromagnetic waves can penetrate into a material.

2. Why is the Paul equation important in skin depth calculation?

The Paul equation is important because it is one of the most commonly used equations for calculating skin depth. It takes into account the material's electrical conductivity, relative permeability, and frequency of the electromagnetic wave.

3. What are the other equations used for skin depth calculation?

Other equations used for skin depth calculation include the Kennelly-Heaviside equation, the Schelkunoff equation, and the Gaussian equation. These equations may give slightly different results compared to the Paul equation due to different assumptions and approximations.

4. How can skin depth confusion be avoided?

To avoid skin depth confusion, it is important to use the same equation consistently when calculating skin depth for a specific material. It is also important to understand the assumptions and limitations of each equation and choose the most appropriate one for the specific application.

5. Can skin depth be experimentally measured?

Yes, skin depth can be experimentally measured using techniques such as eddy current testing or skin effect probes. These methods involve passing an electromagnetic wave through the material and measuring the depth at which the wave is attenuated to a certain level.

Similar threads

Replies
3
Views
1K
  • Classical Physics
Replies
4
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Classical Physics
2
Replies
36
Views
4K
  • Introductory Physics Homework Help
Replies
19
Views
918
  • Special and General Relativity
Replies
2
Views
519
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
10
Views
2K
  • Advanced Physics Homework Help
Replies
4
Views
8K
  • Introductory Physics Homework Help
Replies
10
Views
848
Back
Top