# One Hundred and Fifty Years of Skin Effect
## 5 Conclusions  
The subject of the present paper is current density and current in a group of long conductors. The group is described in Introduction. The publication of [PERSON]'s book [1] marked the beginning of a one hundred and fifty year history of attempts at proposing a method for the calculation of current density in long parallel solid conductors. [PERSON]'s method can only be applied to a solitary conductor connected to an ideal current source, which cannot be implemented. If it is assumed that the current density in the conductors of a loop formed by two conductors is the current density of two solitary conductors, then the accuracy of such an approximation increases with increasing distance of the conductors. In that case, the proximity effect cannot be analysed, and the effect of current density on the result of the calculation of inductance is small because the decisive influence is that of the magnetic flux through the area between the conductors. All the papers published up to now, with the exception of those by the author of this review and his fellow workers, deal with the solitary conductor, or they try to transfer the result of the solitary conductor to a group of conductors or they solve Equation (6) or (7). The current density calculated by these methods is approximate, and its application in the analysis of the proximity effect and in the calculation of inductance is therefore also approximate. The knowledge of exact current density obtained via solving the basic task makes it possible to quantify the proximity effect and thus not only to state that the current density in the conductor is affected by current in the neighbouring conductors. The proximity effect affects the voltage on the inductor, and the calculation of this voltage in terms of self-inductance is highly inaccurate and therefore it is suitable to characterize the inductor by a time-dependent induced voltage instead of self-inductance. The definition in ref. [31] is special in that the skin effect is not defined for conductors but only for the conductor. On the other hand, it is very general because it does not contain any assumption as to the conductor length and shape. It is assumed in the definition that the current in the conductor is alternating, but in ref. [31], item 121-13-18, there is a note 2: \"The skin effect occurs also in the more general case of any time-varying current\". It follows from the specific cases quoted above that the skin effect is not an entirely general phenomenon, the more so because no analysis has so far been made of current density in conductors during transient phenomena and with conductor resistivity that is not constant over the conductor cross section. When using the term skin effect, it would therefore be advisable to state the relevant conditions: the form of the dependence of the voltage or current source on time, the shape of the conductor cross section, the position of the conductors in space, and in the case of transient phenomena, the initial current density Playing with words in connection with the skin effect and the proximity effect can be replaced by an indisputable statement: \"Current density is not constant in conductors that are in a time-varying magnetic field\". The skin effect is connected with the so-called resistance dependence on the frequency of the passing current. A strict distinction needs to be made between the resistance according to [PERSON]'s law and the real component of impedance. For alternating current with non-zero frequency, the resistance according to [PERSON]'s law does not depend on frequency and its value is not equal to the value of the real component of impedance, which depends on frequency. Knowing the current density obtained by the solution of the basic task enables analysis of the phenomena connected with the skin effect, in particular analysing an accurate calculation of voltage on the conductor. This does not mean a refutation of the papers published so far.