### Abstract

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenom-enas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

Original language | English |
---|---|

Title of host publication | Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering |

Publisher | Springer Netherlands |

Pages | 323-332 |

Number of pages | 10 |

ISBN (Print) | 9781402060410 |

DOIs | |

Publication status | Published - 2007 |

### Fingerprint

### Keywords

- eddy currents
- electromagnetism
- fractional calculus
- Skin effect

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering*(pp. 323-332). Springer Netherlands. https://doi.org/10.1007/978-1-4020-6042-7_22

**Electrical skin phenomena : A fractional calculus analysis.** / MacHado, J. A Tenreiro; Jesus, Isabel S.; Galhano, Alexandra; Cunha, J. Boaventura; Tar, J.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering.*Springer Netherlands, pp. 323-332. https://doi.org/10.1007/978-1-4020-6042-7_22

}

TY - CHAP

T1 - Electrical skin phenomena

T2 - A fractional calculus analysis

AU - MacHado, J. A Tenreiro

AU - Jesus, Isabel S.

AU - Galhano, Alexandra

AU - Cunha, J. Boaventura

AU - Tar, J.

PY - 2007

Y1 - 2007

N2 - The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenom-enas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

AB - The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenom-enas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

KW - eddy currents

KW - electromagnetism

KW - fractional calculus

KW - Skin effect

UR - http://www.scopus.com/inward/record.url?scp=70349390185&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349390185&partnerID=8YFLogxK

U2 - 10.1007/978-1-4020-6042-7_22

DO - 10.1007/978-1-4020-6042-7_22

M3 - Chapter

SN - 9781402060410

SP - 323

EP - 332

BT - Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering

PB - Springer Netherlands

ER -