Magnetic field and forces in a pair of parallel conductors

Coufal, Oldřich; Radil, Lukas; Toman, Petr

doi:10.3233/jae-170077

Cited by 5 publications

(5 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The cross section of the outer conductor is the annular ring r o ä[r on , r o0 ], where ] <  r r r in on o0 . In [3,4,12,18] two parallel conductors are examined which are of identical cross sections, symmetrical with respect to the straight line and with symmetrical resistivity. The calculation method in [3,4,12,18] is formulated for cross sections of arbitrary shape, with specific results given for rectangular and circular cross sections.…”

Section: Comparison Of Newly Obtained Results With Published Resultsmentioning

confidence: 99%

Current density in a group of long parallel conductors

Coufal

2019

Phys. Scr.

View full text Add to dashboard Cite

An original method is proposed for the calculation of current density in a finite number of long parallel solid conductors of arbitrary cross section. Some pairs of the conductors under examination can be connected to a voltage source; they are active. The other conductors are passive. The currents, voltages and magnetic fields are assumed to be quasi-stationary and the displacement current is neglected. The permeability of the conductor material is constant and equals the vacuum permeability. No method has so far been published that would allow an exact calculation of current density in all the cases that satisfy the above assumptions. The application of the method is demonstrated by solving an example with two active conductors, one of which is of circular and the other of rectangular cross section, while a third passive conductor is of rectangular cross section.

show abstract

Section: Comparison Of Newly Obtained Results With Published Resultsmentioning

confidence: 99%

Current density in a group of long parallel conductors

Coufal

2019

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…C. Maxwell proposed a method for the calculation of current density in a solitary conductor [15]. Hundreds of works have since been published (more recently, e.g., [1,[16][17][18][19][20][21][22][23][24]) that deal with the calculation of current density in one or two conductors, and exceptionally in more conductors. The calculation of current density in one conductor is accurate, but it can only be applied to the solitary conductor connected to the ideal current source, which, however, cannot be implemented [1].…”

Section: Discussionmentioning

confidence: 99%

“…The calculation of current density in one conductor is accurate, but it can only be applied to the solitary conductor connected to the ideal current source, which, however, cannot be implemented [1]. The published methods, with the exception of those in [1,3,24], are approximate, with the current density error unknown. The self-inductance of two conductors cannot be calculated without accurate current density [2] and thus approximate formulae continue to be used for the calculation of self-inductance of two coaxial conductors and two circular cross section conductors [2].…”

Section: Discussionmentioning

confidence: 99%

Transient Current Density in a Pair of Long Parallel Conductors

Coufal¹

2021

Applied Sciences

Self Cite

View full text Add to dashboard Cite

Two infinitely long parallel conductors of arbitrary cross section connected to a voltage source form a loop. If the source voltage depends on time, then due to induction there is no constant current density in the loop conductors. It is only recently that a method has been published for accurately calculating current density in a group of long parallel conductors. The method has thus far been applied to the calculation of steady-state current density in a loop connected to a sinusoidal voltage source. In the present article, the method is used for an accurate calculation of transient current using transient current density. The transient current is analysed when connecting and short-circuiting the sources of sinusoidal, constant and sawtooth voltages. For circular cross section conductors, the dependences of maximum current density, maximum current and the time of achieving steady state on the source frequency, the distance of the conductors and their resistivity when connecting the source of sinusoidal voltage are examined.

show abstract

“…If the surface of the conductors is parallel with the planes xy and xz, then the current density, J(x, y), may oscillate for y = const, as can be seen in Figure 3 in ref. [21].…”

Section: Solitary Conductor Conceptmentioning

confidence: 99%

“…The determination of independent fluxes is described in [9][10][11][12]. If in the calculation of current density in a solitary conductor or in a loop formed by two conductors the conductor cross sections are symmetrical and the values of conductor resistivity are also symmetrical, the determination of independent fluxes is simple if symmetry is used [13][14][15][16][17][18][19][20][21].…”

mentioning

confidence: 99%

One Hundred and Fifty Years of Skin Effect

Coufal

2023

Applied Sciences

Self Cite

View full text Add to dashboard Cite

In 1873, J.C. Maxwell derived relations for current density and current in a solitary long cylindrical conductor supplied with variable current. According to Maxwell, the current density in a conductor increases towards the conductor surface. This phenomenon is called the skin effect. The skin effect affects in particular the inductance of a line formed by one or several long parallel conductors. A number of papers have been published regarding the skin effect and its effect on inductance. Another phenomenon, closely related to the skin effect, is the proximity effect, which refers to the dependence of the current density in a conductor on the proximity of other conductors through which a time-variable current is flowing. Many published papers deal with the calculation of current density in two conductors, using the method for calculating current density in a solitary conductor. 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. It follows from the analysis performed that the skin effect is not a general characteristic of current density in long conductors, except for in the solitary conductor. This conclusion affects the knowledge of the phenomena associated with the skin effect.

show abstract

Magnetic field and forces in a pair of parallel conductors

Cited by 5 publications

References 6 publications

Current density in a group of long parallel conductors

Current density in a group of long parallel conductors

Transient Current Density in a Pair of Long Parallel Conductors

One Hundred and Fifty Years of Skin Effect

Contact Info

Product

Resources

About