# One Hundred and Fifty Years of Skin Effect
## 1 Introduction  
Current density in a conductor through which variable current passes increases towards the conductor surface. This phenomenon is called the skin effect. The skin effect is inextricably linked with current density. It is therefore strange that the existence of this phenomenon is generally assumed, even though an exact method for the calculation of current density was until recently known only for the infinitely long solitary conductor of circular cross section with constant resistivity. The aim of the present paper is an analysis of current density in long parallel conductors of arbitrary cross section with respect to the skin effect and other related phenomena. The starting point of the analysis has been the recently proposed accurate method for the calculation of current density in the conductors under investigation. In 1873, [PERSON] published the book \"A Treatise on Electricity and Magnetism\" [1]. The book is in two volumes and divided into articles; it was published in three editions [1; 2; 3]. The next editions, for example [4], are unabridged republications of the third edition [3]. Articles 689 and 690 in [1; 2; 3] deal with the calculation of current density and current in a solitary straight infinitely long conductor of circular cross section supplied with variable current. According to [PERSON], the amplitude of the current density of alternating current (of non-zero frequency) passing through a conductor increases towards the surface of the conductor. This phenomenon is called the skin effect. The term skin effect is not used in [1; 2; 3]; it was probably introduced later. For example, according to [5], [PERSON] published a paper in 1883 [6] which dealt with the motions of electricity produced in a spherical conductor by any electric or magnetic operations outside it, which was later to be known as the skin effect [5]. [PERSON], who prepared thethird edition of [PERSON]'s book, added in the form of a footnote a derivation of the formula for calculating the inductance of a cylindrical conductor supplied with sinusoidal current. As part of this derivation, he also obtained a relation for the dependence of conductor resistance on the frequency of the supply current. Another phenomenon closely related to the skin effect is the proximity effect, which refers to the dependence of current density in the conductor on the proximity of further conductors through which a time-varying current flows. Many published papers deal with the approximate calculation of current density in two conductors using the method for calculating current density in a solitary conductor. What is addressed in papers on the calculation of current density in two conductors is usually the skin effect, the proximity effect and the dependence of resistance on frequency, and their effect on self-inductance. Since the publication of the book [1], a plethora of articles and parts of books have been published that deal with the subject matter of the present review. In [7], published in 1959, the list of references contains 454 items, and one recent item is [8]. Thus, it is not possible to evaluate all the relevant papers. All the phenomena given above can be analysed and quantitatively described based on the knowledge of current density in conductors, and therefore the method for calculating current density in a group of conductors is of fundamental significance. An accurate method for calculating current density in conductors forming a group has only recently been published [9; 10; 11; 12]. The subject of investigation in [9; 10; 11; 12] is a physical and mathematical model of a task referred to as the basic task.