Untitled

Assis, A. K. T.; Rodrigues, Waldyr A.; Mania, A.

doi:10.1023/a:1018874523513

Cited by 76 publications

(46 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…(27) and (28), agree with the known case of a long straight cylindrical conductor carrying a steady current, Eqs. (12) and (13) of [9]. The electric potential of the thin toroid approximation without current agrees with the known result of a charged wire, [23, p. 93].…”

Section: Discussionsupporting

confidence: 83%

“…(27) and (28) can be compared to Eqs. (12) and (13) of Assis, Rodrigues and Mania, [9], respectively. They have studied the case of a long straight cylindrical conductor of radius r 0 carrying a constant current, in cylindrical coordinates (ρ , ϕ, z) (note that the conversions from toroidal to cylindrical coordinates in this approximation areη ≈ −ρ andφ ≈ẑ).…”

Section: Thin Toroid Approximationmentioning

confidence: 99%

“…318 and 509-511], [3], [4, pp. 336-337] and [5]; solenoid with azimuthal current, [2, p. 318] and [6]; transmission line, [7, p. 262] and [8]; straight wire, [9]; and conductor plates, [10]. The only cases solved in the literature where the geometry of the conductor is finite are those of a finite coaxial cable considered by Jackson, [11], and that of a toroidal conducting ring, [12].…”

Section: Toroidal Ringmentioning

confidence: 99%

“…where the coefficients A p and B pq are given by, respectively: (9) where δ wp is the Kronecker delta, which is zero for w = p and one for w = p. The functions P q For the region inside the hollow toroid (that is, η > η 0 ), the potential is given by:…”

Section: Toroidal Ringmentioning

confidence: 99%

See 3 more Smart Citations

Surface charges and external electric field in a toroid carrying a steady current

Hernandes¹,

Assis²

2004

Braz. J. Phys.

Self Cite

View full text Add to dashboard Cite

We solve the problem of a resistive toroid carrying a steady azimuthal current. We use standard toroidal coordinates, in which case Laplace's equation is R-separable. We obtain the electric potential inside and outside the toroid, in two separate cases: 1) the toroid is solid; 2) the toroid is hollow (a toroidal shell). Considering these two cases, there is a difference in the potential inside the hollow and solid toroids. We also present the electric field and the surface charge distribution in the conductor due to this steady current. These surface charges generate not only the electric field that maintains the current flowing, but generate also the electric field outside the conductor. The problem of a toroid is interesting because it is a problem with finite geometry, with the whole system (including the battery) contained within a finite region of space. The problem is solved in an exact analytical form. We compare our theoretical results with an experimental figure demonstrating the existence of the electric field outside the conductor carrying steady current. Toroidal RingThe electric field outside conductors with steady currents has been studied in a number of cases. Here we consider the case of the conducting toroid with a steady current. Our goal is to find the electric potential inside and outside the toroid, and from the potential we can find the electric field and surface charges. More details about this problem and its analytical solution can be found in [12].Consider a toroidal conductor with uniform resistivity. It has greater radius R 0 and smaller radius r 0 and carries a steady current I in the azimuthal direction, flowing along the circular loop. The toroid has rotational symmetry around the z-axis and is centered in the plane z = 0. The battery that maintains the current is located at ϕ = π rad, see Fig. 1. Air or vacuum surrounds the conductor.The electric potential φ can be calculated using toroidal coordinates (η, ξ, ϕ) [13, p. 112], defined by:(1) Figure 1. A toroidal ohmic conductor with symmetry axis z, smaller radius r 0 (m) and greater radius R (m). A thin battery is located at ϕ = π rad maintaining constant potentials (represented as the "+" and "-" signs) in its extremities. A steady current flows azimuthally in this circuit loop in the clockwise direction, from ϕ = +π rad to ϕ = −π rad.Here, a is a constant such that when η → ∞ we have the circle x = a cos ϕ, y = a sin ϕ and z = 0. The toroidal coordinates can have the possible values: 0 ≤ η < ∞, −π rad ≤ ξ ≤ π rad and −π rad ≤ ϕ ≤ π rad. We take η 0 as a constant that described the toroid surface in toroidal coordinates. The internal (external) region of the toroid is characterized by η > η 0 (η < η 0 ).

show abstract

Section: Discussionsupporting

confidence: 83%

Section: Thin Toroid Approximationmentioning

confidence: 99%

Section: Toroidal Ringmentioning

confidence: 99%

Section: Toroidal Ringmentioning

confidence: 99%

See 2 more Smart Citations

Surface charges and external electric field in a toroid carrying a steady current

Hernandes¹,

Assis²

2004

Braz. J. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Russell [8] generaliza los resultados de Sommerfeld para un sistema de conductores paralelos e infinitos, mientras que Ferreira y Figueredo [9] adaptan el análisis de Sommerfeld para un cable coaxial semi-infinito cerrado en uno de sus extremos por un disco perfectamente conductor. Jefimenko [10] calcula los campos en el interior de un circuito formado por placas paralelas, Assis et al [11] deducen los campos afuera de las placas y Assis et al [12], analizan las cargas superficiales y los campos de un hilo resistivo rectilíneo de sección circular. Heald [13] encuentra los campos afuera y adentro de un circuito cilíndrico con corriente azimutal y el flujo de energía que va desde la batería hacia la superficie del cilindro resistivo.…”

Section: Introductionunclassified

Las cargas superficiales y el flujo de energía en un circuito simple

Welti¹

2005

Rev. Bras. Ens. Fis.

View full text Add to dashboard Cite

El interés en el estudio de la distribución de las cargas superficiales sobre los conductores que transportan una corriente y su utilidad para la comprensión conceptual del comportamiento de los circuitos se han incrementado recientemente. Numerosos trabajos y textos presentan resultados cualitativos, analíticos y numéricos para diferentes geometrías de la estructura del circuito. Se presentan aquí los resultados analíticos para un circuito simple formado por placas rectangulares. Esta geometría permite determinar no solo la distribución de las cargas superficiales que crean el campo en el interior de los conductores, sino también el flujo de energía que se dirige desde la fuente hasta los elementos resistivos del circuito. Palabras clave: circuitos, cargas superficiales, campo eléctrico, flujo de energía.The interest in the study of the superficial charges's distribution on the conductors that transport a current and its utility for the conceptual comprehension of the circuits's behavior have been increased recently. Numerous works and texts present numerical, analytic, and qualitative results for different geometries of the circuit's structure. The analytic results for a simple circuit formed by rectangular plates are presented here. This geometry permits to determine not only the distribution of the superficial charges that create the field in the interior of the conductors, but also the flow of energy that is directed since the source to the resistive elements of the circuit.

show abstract

In‐Plane Potential Gradient Induces Low Frictional Energy Dissipation during the Stick‐Slip Sliding on the Surfaces of 2D Materials

Yang

Bian

et al. 2019

Small

View full text Add to dashboard Cite

Understanding the nanoscale friction properties of 2D materials and further manipulating their friction behaviors is of great significance for the development of various micro/nanodevices. Recent studies, taking advantage of the close relationship between friction and surface charges, use an external out‐of‐plane electric field to control the interfacial friction. Nevertheless, friction increases with the application of the out‐of‐plane electric field in most cases. Here, an in‐plane potential gradient is applied for the investigation of the contribution of electric charges to friction on the surfaces of 2D materials. Experimental results show that the friction between an atomic force microscope tip and the flakes of 2D materials decreases with the application of the in‐plane potential gradient, and the higher the potential gradient, the greater the friction decrease. By comparing the in situ atomic‐level stick‐slip maps before and after the application of the in‐plane potential gradient, it is proposed that the promotion of low friction dissipative motion during the stick‐slip process owing to the presence of the potential gradient gives rise to the friction reduction. These results not only help to reveal the origin of friction, but also provide a novel way to manipulate friction through an electrically‐controlled sliding process.

show abstract

Untitled

Cited by 76 publications

References 22 publications

Surface charges and external electric field in a toroid carrying a steady current

Surface charges and external electric field in a toroid carrying a steady current

Las cargas superficiales y el flujo de energía en un circuito simple

In‐Plane Potential Gradient Induces Low Frictional Energy Dissipation during the Stick‐Slip Sliding on the Surfaces of 2D Materials

Contact Info

Product

Resources

About