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

Akım yoğunluğu, farklı elektriksel iletkenliklere sahip bir arayüz boyunca süreksiz hale gelir.
Sabit akımlar için, akım yoğunluğunun sapması sıfırdır. Bu nedenle, akım yoğunluğunun normal bileşeni sınır boyunca süreklidir.
Elektrik alanın teğetsel bileşeninin bir arayüz boyunca sürekli olduğunu hatırlayın. Elektrik alanını akım yoğunluğu ve elektriksel iletkenlik cinsinden ifade etmek, akım yoğunluğunun teğetsel bileşeni için sınır koşulunu verir.
Şimdi, elektrik yer değiştirmesinin normal bileşeni arayüz boyunca süreksizdir. Bu nedenle, elektrik alanının normal bileşeni de bir arayüz boyunca süreksizdir.
Yine elektrik alan ve akım yoğunluğu ifadesi kullanılarak, akım yoğunluğunun normal bileşeni için sınır koşulu geçirgenlik ve iletkenlik açısından elde edilir.
Farklı iletkenliklere ve/veya geçirgenliklere sahip bir arayüz boyunca bir yüzey yük yoğunluğunun oluşturulduğunu gösterir.
Aynı iletkenlik ve geçirgenlik değerlerine sahip veya iletkenliğe eşit geçirgenlik oranına sahip bir arayüz için yüzey yük yoğunluğu sıfırdır.

<ol>
	<li>Ida, Nathan, Mühendislik Elektromanyetikleri, 3. Baskı, Springer. s. 355-356</li>
	<li>Cheng, David K., Alan ve Dalga Elektromanyetik, Addison-Wesley Yayıncılık Şirketi, s. 183.</li>
</ol>

akım yoğunluğu için sınır koşulları

Farklı elektrik iletkenliklerine sahip malzemelerin arayüzünde akım yoğunluğu kesintili hale gelir. Akım yoğunluğunun normal bileşeni sınırdan geçerken kesintisizdir.

<img alt="Equation1" src="/files/ftp_upload/14187/14187_Equation_1.png" style="text-align: center; height: 24px;" />

Ancak, akım yoğunluğunun teğetsel bileşenleri arayüz boyunca kesintilidir.

<img alt="Equation2" src="/files/ftp_upload/14187/14187_Equation_2.png" style="text-align: center; height: 55px;" />

İki iletken medyanın ayrıldığı bir arayüz düşünün; bu medyanın iletkenlikleri σ1 ve σ2 olsun. Arayüzdeki istikrarlı akım yoğunluğu<img height="22" src="file:///C:/Users/tirth/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" width="11" />, P1 noktasında medya 1'de P2 noktasında ise medya 2'deki akım yoğunluğu normalle α2 açı yapar.

<img alt="Figure1" src="/files/ftp_upload/14187/14187_figure_1.png" style="text-align: center" />

Akım yoğunluğunun normal ve teğetsel bileşenleri aşağıdaki denklemleri verir:

<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;" />

İki denklemin oranını alarak, her iki medya için elektrik iletkenliklerinin ifadesi elde edilir.

<img alt="Equation5" src="/files/ftp_upload/14187/14187_Equation_5.png" style="text-align: center; height: 40px;" />

Eğer medya 1'in elektrik iletkenliği medya 2'den büyükse, α2 açısı sıfıra yakınsar. Bu, akım yoğunluğunun<img height="22" src="file:///C:/Users/tirth/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" width="11" /> İletken 1'in yüzeyine normal olduğu anlamına gelir.

Akım yoğunluğu için Sınır Koşulları

Akım yoğunluğu, farklı elektriksel iletkenliklere sahip malzemelerden oluşan bir arayüz boyunca süreksiz hale gelir. Akımın normal bileşeni ...

Education

JoVE Core

Physics

Fizik

Unit 1

Ünite 1

Current and Resistance

Akım ve Direnç

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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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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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