Name: current density at conductivity boundaries
Uploaded: 2023-09-18T17:11:18.000Z
Duration: 1 min 25 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

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Motion and Stability- Forces and Interactions

PS.PSc.6.3

Boundary Conditions for Current Density

Плотность тока становится прерывистой на границе раздела с разной электропроводностью.
Для стационарных токов расходимость плотности тока равна нулю. Таким образом, нормальная составляющая плотности тока непрерывна по всей границе.
Вспомним, что тангенциальная составляющая электрического поля непрерывна на всей границе раздела. Выражение электрического поля в терминах плотности тока и электропроводности дает граничное условие для тангенциальной составляющей плотности тока.
Теперь нормальная составляющая электрического смещения прерывиста по всей границе раздела. Таким образом, нормальная составляющая электрического поля также прерывиста по всей границе раздела.
Опять же, используя выражение электрического поля и плотности тока, граничное условие для нормальной составляющей плотности тока получается в терминах диэлектрической и проводимости.
Он показывает, что поверхностная плотность заряда создается на границе раздела с различной проводимостью и/или диэлектрической проницаемостью.
Поверхностная плотность заряда равна нулю для границы раздела с теми же значениями проводимости и диэлектрической проницаемости или с равным отношением диэлектрической проницаемости к проводимости.

<ol>
	<li>Ида, Натан, Инженерная электромагнетизм, 3-е издание, Springer. стр. 355-356</li>
	<li>Ченг, Дэвид К., Полевая и волновая электромагнетизм, Addison-Wesley Publishing Company, стр. 183.</li>
</ol>

Граничные условия для плотности тока

Плотность тока становится разрывной вдоль границы материалов с различной электропроводностью. Нормальная компонента плотности тока непрерывна вдоль границы.

<img alt="Equation1" src="/files/ftp_upload/14187/14187_Equation_1.png" style="text-align: center; height: 24px;" />

Однако, касательные компоненты плотности тока являются разрывными вдоль интерфейса.

<img alt="Equation2" src="/files/ftp_upload/14187/14187_Equation_2.png" style="text-align: center; height: 55px;" />

Рассмотрим интерфейс, разделённый двумя проводящими средами с проводимостями σ1 и σ2. Постоянная плотность тока на интерфейсе составляет <img height="22" src="file:///C:/Users/tirth/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" width="11" /> в среде 1 в точке P11 с нормалью. Плотность тока <img height="22" src="file:///C:/Users/tirth/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" width="11" />  в точке P2 в среде 2 образует угол α2 с нормалью.

<img alt="Figure1" src="/files/ftp_upload/14187/14187_figure_1.png" style="text-align: center" />

Нормальная и тангенциальная компонента плотности тока даёт следующие уравнения:

<img alt="Equation3" src="/files/ftp_upload/14187/14187_Equation_3.png" style="text-align: center; height: 16px;" />

<img alt="Equation4" src="/files/ftp_upload/14187/14187_Equation_4.png" style="text-align: center; height: 16px;" />

Пользуясь отношением этих двух уравнений, получаем выражение для электрической проводимости в обеих средах.

<img alt="Equation5" src="/files/ftp_upload/14187/14187_Equation_5.png" style="text-align: center; height: 40px;" />

Если электрическая проводимость среды 1 больше, чем у среды 2, угол α2  нормальна к поверхности проводника 1.

Плотность тока становится прерывистой на границе раздела материалов с разной электропроводностью. Нормальная составляющая текущего...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Current and Resistance

Ток и сопротивление

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

current density at conductivity boundaries

Current density at a boundary changes when two conducting materials have different electrical conductivities. The normal component of current density stays continuous across the interface. The tangential component, which runs along the surface, becomes discontinuous across the boundary.

Consider two conducting media with conductivities σ1 and σ2 separated by an interface. At point P1 in medium 1, the steady current density makes an angle α1 with the normal. At point P2 in medium 2, the current density makes an angle α2 with the normal.

The normal and tangential parts of the current density lead to two equations. Taking the ratio of those equations gives the relation for the electrical conductivities in both media. If medium 1 has a greater conductivity than medium 2, angle α2 approaches zero. In that case, the current density becomes normal to the surface of conductor 1.

Current Density at Conductivity Boundaries

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Current density at a boundary changes when two conducting materials have different electrical conductivities. The normal component of current density stays continuous across the interface. The tangential component, which runs along the surface, becomes discontinuous across the boundary. Consider two conducting media with conductivities σ1 and σ2 separated by an interface. At point P1 in medium 1, the steady current density makes an angle α1 with the normal. At point P2 in medium 2, the current...

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Learn how current density behaves at the boundary between two conductors. See why the normal component stays continuous and the tangential component changes.

Current Density at Conductivity Boundaries | JoVE K12

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Current Density at Conductivity Boundaries

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