# Angular Spectral Density and Information Entropy for Eddy Current Distribution

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Energy of Field Distribution Density of a Multidimensional Vector in a Multidimensional Space

## 3. Probability Density Discretization

## 4. Information Entropy of Energy Allocation of a Vector Field

## 5. Two-Dimensional EC Vector in a Two-Dimensional Plane

## 6. Acquisition of EC Vector

## 7. Results and Discussion

#### 7.1. Analysis of Angular Spectral Density along the x-Axis

#### 7.2. Angular Spectral Density

#### 7.3. Information Entropy along the x-Axis

#### 7.4. Information Entropy of the Whole Interaction Domain

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Angle spectrum density along the x-axis of different exciting coils and different widths of the interaction domain: (

**a**) line exciting, $L=5\text{}\mathrm{mm}$; (

**b**) line exciting, $L=10\text{}\mathrm{mm}$; (

**c**) line exciting, $L=20\text{}\mathrm{mm}$; (

**d**) line exciting, $L=25\text{}\mathrm{mm}$; (

**e**) circle exciting, $L=40\text{}\mathrm{mm}$; (

**f**) circle exciting, $L=5\text{}\mathrm{mm}$; (

**g**) circle exciting, $L=10\text{}\mathrm{mm}$; (

**h**) circle exciting, $L=20\text{}\mathrm{mm}$; (

**i**) circle exciting, $L=25\text{}\mathrm{mm}$; (

**j**) circle exciting, $L=40\text{}\mathrm{mm}$; (

**k**) Koch exciting, $L=5\text{}\mathrm{mm}$; (

**l**) Koch exciting, $L=10\text{}\mathrm{mm}$; (

**m**) Koch exciting, $L=20\text{}\mathrm{mm}$; (

**n**) Koch exciting, $L=25\text{}\mathrm{mm}$; (

**o**) Koch exciting, $L=40\text{}\mathrm{mm}$.

**Figure 3.**Total angle spectrum for different exciting coils and different widths of the interaction domain. (

**a**) $L=5\text{}\mathrm{mm}$; (

**b**) $L=10\text{}\mathrm{mm}$; (

**c**) $L=20\text{}\mathrm{mm}$; (

**d**) $L=25\text{}\mathrm{mm}$; (

**e**) $L=40\text{}\mathrm{mm}$.

**Figure 4.**Information entropy $H\left(x\right)$ for different exciting coils and different widths of the interaction domain. (

**a**) $L=5\text{}\mathrm{mm}$; (

**b**) $L=10\text{}\mathrm{mm}$; (

**c**) $L=20\text{}\mathrm{mm}$; (

**d**) $L=25\text{}\mathrm{mm}$; (

**e**) $L=40\text{}\mathrm{mm}.$

**Figure 5.**Total information entropy $H$ for different exciting coils and different widths of the interaction domain.

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**MDPI and ACS Style**

Chen, G.; Zhang, W.
Angular Spectral Density and Information Entropy for Eddy Current Distribution. *Entropy* **2016**, *18*, 392.
https://doi.org/10.3390/e18110392

**AMA Style**

Chen G, Zhang W.
Angular Spectral Density and Information Entropy for Eddy Current Distribution. *Entropy*. 2016; 18(11):392.
https://doi.org/10.3390/e18110392

**Chicago/Turabian Style**

Chen, Guolong, and Weimin Zhang.
2016. "Angular Spectral Density and Information Entropy for Eddy Current Distribution" *Entropy* 18, no. 11: 392.
https://doi.org/10.3390/e18110392