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

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

motion-and-stability-forces-and-interactions

Motion and Stability- Forces and Interactions

PS.PSc.6.3

Boundary Conditions for Current Density

전류 밀도는 전기 전도도가 다른 계면에서 불연속적이 됩니다.
정상 전류의 경우 전류 밀도의 발산은 0입니다. 따라서 전류 밀도의 수직 구성 요소는 경계를 가로질러 연속적입니다.
전기장의 접선 구성 요소는 인터페이스를 가로질러 연속적이라는 것을 기억하십시오. 전류, 밀도 및 전기 전도도의 관점에서 전기장을 표현하면 전류 밀도의 접선 구성 요소에 대한 경계 조건이 제공됩니다.
이제 전기 변위의 수직 구성 요소는 계면에서 불연속적입니다. 따라서 전기장의 정상 구성 요소도 계면에서 불연속적입니다.
다시 말하지만, 전기장과 전류 밀도의 표현을 사용하여 전류 밀도의 수직 구성 요소에 대한 경계 조건은 유전율 및 전도성 측면에서 얻어집니다.
이는 표면 전하 밀도가 서로 다른 전도성 및/또는 유전율을 갖는 계면에서 생성됨을 보여줍니다.
표면 전하 밀도는 전도도 및 유전율 값이 동일하거나 유전율 대 전도성 비율이 동일한 계면에 대해 0입니다.

<ol>
	<li>Ida, Nathan, Engineering Electromagnetics, 3판, Springer. 355-356쪽</li>
	<li>Cheng, David K., Field and Wave Electromagnetics, Addison-Wesley Publishing Company, pp. 183.</li>
</ol>

전류 밀도의 경계 조건

전류 밀도는 전기 전도도가 다른 재료의 경계면에서 불연속적이 됩니답안 전류 밀도의 일반 구성 요소는 경계를 넘어 연속적입니답안

<img alt="Equation1" src="/files/ftp_upload/14187/14187_Equation_1.png" style="text-align: center; height: 24px;" />

그러나 전류 밀도의 접선 성분은 인터페이스 전체에서 불연속적입니답안

<img alt="Equation2" src="/files/ftp_upload/14187/14187_Equation_2.png" style="text-align: center; height: 55px;" />

전도도가 '1 및 '2인 두 개의 전도 매체로 분리된 인터페이스를 생각해 보세요. 인터페이스의 안정된 전류 밀도는 <img height="22" src="file:///C:/Users/tirth/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" width="11" />, P1 지점의 매체 1에 있습니답안 법선과 각도 '1을 만듭니답안 현재 밀도 <img height="22" src="file:///C:/Users/tirth/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" width="11" />  매체 2의 P2 지점에서 법선과 각도 α2를 이룹니답안

<img alt="Figure1" src="/files/ftp_upload/14187/14187_figure_1.png" style="text-align: center">

전류 밀도의 법선 및 접선 성분은 다음과 같은 방정식을 제공합니답안

<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;" />

두 방정식의 비율을 사용하여 두 매체의 전기 전도도에 대한 표현식을 얻습니답안

<img alt="Equation5" src="/files/ftp_upload/14187/14187_Equation_5.png" style="text-align: center; height: 40px;" />

매질 1의 전기 전도성이 매질 2의 전기 전도성보다 크면 각도 '2는 0에 가까워집니답안 이는 현재 밀도 <img height="22" src="file:///C:/Users/tirth/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" width="11" /> 도체 1의 표면에 수직입니답안

전류 밀도는 전기 전도도가 다른 재료의 계면에서 불연속적이 됩니다. 현재의 정상적인 구성 요소 ...

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

Current and Resistance

전류와 저항

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

current-density-at-conductivity-boundaries

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boundary conditions for current density

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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