Charges and fields in a current-carrying wire

Abstract

Charges and fields in a straight, infinite, cylindrical wire carrying a steady current are determined in the rest frames of ions and electrons, starting from the standard assumption that the net charge per unit length is zero in the lattice frame and taking into account a self-induced pinch effect. The analysis presented illustrates the mutual consistency of classical electromagnetism and Special Relativity. Some consequences of the assumption that the net charge per unit length is zero in the electrons frame are also briefly discussed. IntroductionAs is well known, combining Coulomb's law, charge invariance and the transformation law of a pure relativistic three-force [1,2], one can derive the correct equation for the force with which a point charge in uniform motion acts on any other point charge in arbitrary motion, and thus recognize both the E E E and B B B fields of a uniformly moving point charge and the corresponding Lorentz force expression [3][4][5]. Thus one can prove indirectly, without introducing general transformations for E E E and B B B, that the Lorentz force expression, f f f L ≡ qE E E + qu u u ×B B B, transforms in the same way as the time derivative of the relativistic momentum of a particle with time independent mass, in the special case of E E E and B B B due to a uniformly moving point charge. Following the same line of reasoning, the so-called relativistic nature of the magnetic field is often illustrated by discussing the force on a charged particle outside a current-carrying wire, or the force between two parallel current-carrying wires [5][6][7][8]. (Note that in the latter case, contrary to the widespread opinion,

Charge Relaxation in Biological Tissues with Extremely High Permittivity

“…The author is aware that a self-induced Hall effect is also present within each wire [Matzek 1968, Peters 1985, Hernández 1988, Gabuzda 1993, Redžić 2012], but, for the purpose of the paper, it would not introduce any significant modification to the discussion).…”

“…We imagine that the sphere translates along the x-axis, through a stationary and uniform magnetic field (with B = 1 T) directed along the y-axis. As shown by ( 6)-( 10), in its own reference frame the sphere experiences an electric field E 0 = E 0ẑ , whose magnitude follows the time behavior of v. This happens because B is stationary and we assume that the currents induced in the biological material are too low to perturb the distribution of B impressed by the external sources [Cobos Sánchez 2009, 2012, Chiampi 2011, Laakso 2013, Trakic 2014, Zilberti 2015.…”

Lorentz Force from a Current-Carrying Wire on a Charge in Motion under the Assumption of Neutrality in the Symmetrical Frame of Reference

“…The question of the frame of reference, in which the current-carrying wire is neutral, has been the subject of debate in the past years [2]- [10]. Some authors suggest that a neutral wire corresponds to the rest reference frame of the lattice of positive ions (e.g., [2] [6] [7] [8]), considering that electrons are a free ensemble and, therefore, their distances do not change upon acceleration [3].…”

“…The question of the frame of reference, in which the current-carrying wire is neutral, has been the subject of debate in the past years [2]- [10]. Some authors suggest that a neutral wire corresponds to the rest reference frame of the lattice of positive ions (e.g., [2] [6] [7] [8]), considering that electrons are a free ensemble and, therefore, their distances do not change upon acceleration [3]. Others (e.g., [4] [9]) assume that the distances between electrons are also subject to the Lorentz contraction and, therefore, the wire is neutral only in a symmetrical frame of reference in which both electrons and protons have the same speed but move in opposite directions.…”

“…It is therefore necessary to investigate the mechanisms involved in the transition process from no-current wire to current-carrying wire to answer the question of the neutral frame. A more detailed discussion about the issue of the determination of the reference frame in which the current-carrying wire is neutral can be found in [2] and [3].…”