Name: magnetic flux linkage in solid conductors
Uploaded: 2024-11-21T14:54:23.000Z
Duration: 1 min 24 s
Channel: JoVE

固体の円筒形導体のインダクタンスを計算するには、半径rの非磁性通電導体の1メートルの断面を考え、端部の影響を無視して均一な電流密度を仮定します。
アンペアの法則は、導体内の一定の同心円磁場を計算します。
均一な電流分布が与えられると、磁場と磁束密度が決定されます。
次に、単位長さあたりの微分磁束が計算され、導体内の総磁束結合が決定されます。
これにより、単位長さあたりの導体の内部インダクタンスを計算できます。
導体の外側の磁場を見つけるために、アンペアの法則がすべての電流を囲む輪郭に適用されます。これは、磁束密度、微分磁束、および導体外の磁束リンケージを計算するのに役立ちます。
2つの外部ポイント間で積分すると、外部磁束リンケージと、その結果として単位長さあたりの外部インダクタンスが得られます。
外部ポイントでの全磁束結合は、内部と外部の磁束結合の合計であり、これが合計インダクタンスを決定します。
最後に、それぞれが電流を流し、合計電流がゼロに等しい円筒形導体の配列を考慮すると、磁束リンケージが計算されます。

インダクタンス: 固体円筒導体

Inductance: Solid Cylindrical Conductor

固体円筒導体のインダクタンスを計算するには、半径 r の非磁性の電流伝導導体における 1 m のセクションを考えます。端部効果を無視し、均一な電流密度を想定すると、アンペールの法則によって導体内の磁場を判定できます。この法則は、磁場の強度 H が導体内で同心円状かつ一定であることを示しています。

均一な電流分布が与えられれば、導体内の磁場 H_x と磁束密度 B_x が計算されます。次に、導体内の単位長さあたりの微分磁束が計算され、総内部磁束鎖交数が導かれ、単位長さあたりの内部インダクタンスが導出されます。

<img alt="Equation1" src="/files/ftp_upload/16141/16141_Equation%201.svg" style="height: 28px;">

導体の外側の磁場を決定するには、電流全体を囲む輪郭にアンペールの法則を適用します。これにより、導体の外側の磁束密度と差動磁束を計算できます。2 つの外部点間でこれらの値を積分すると、外部磁束結合と、結果として生じる単位長さあたりの外部インダクタンスが得られます。

<img alt="Equation2" src="/files/ftp_upload/16141/16141_Equation%202.svg" style="height: 28px;">

外部点における総インダクタンスは、内部磁束結合と外部磁束結合の合計です。この包括的なアプローチにより、総インダクタンスを正確に決定できます。

<img alt="Equation3" src="/files/ftp_upload/16141/16141_Equation%203.svg" style="height: 28px;">

円筒状の導体の配列を考えた場合、各導体が電流を流し、合計電流がゼロになる場合、各導体からの寄与を合計して磁束鎖交を計算します。これにより、複雑な導体構成のインダクタンスを正確に計算できます。これは、電気システムのパフォーマンスと効率を最適化するために不可欠です。この方法は、内部インダクタンスと外部インダクタンスを組み合わせて、実際のアプリケーションでのインダクタンスを完全に理解できるようにします。

固体の円筒形導体のインダクタンスを計算するには、半径r、...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Transmission Line Parameters

伝送線路パラメータ

KEY TERMS AND CONCEPTS

主要用語と概念

magnetic flux linkage in solid conductors

Magnetic flux linkage in a solid cylindrical conductor is found by combining the field inside the wire with the field around it. The method uses a 1-meter section of a non-magnetic conductor with radius r. It also assumes the current is spread uniformly and ignores end effects.

Inside the conductor, Ampere's law is used to find the magnetic field intensity H. The field is concentric and constant within the conductor. From H, the magnetic flux density B inside the wire is calculated. The differential flux per unit length is then found, and this leads to the total internal flux linkages. These linkages give the internal inductance per unit length.

The same law is then applied outside the conductor. A contour that encloses the full current is used to calculate the magnetic flux density beyond the wire. The differential flux in the outer region is integrated between two external points. This gives the external flux linkages and the external inductance per unit length.

The total inductance at an external point is the sum of the internal and external flux linkages. For an array of cylindrical conductors, the flux linkage is found by adding the contribution from each conductor. In that case, each conductor carries current so the total current equals zero. This approach gives a complete inductance calculation for practical conductor arrangements.

Magnetic Flux Linkage in Solid Conductors

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Magnetic flux linkage in a solid cylindrical conductor is found by combining the field inside the wire with the field around it. The method uses a 1-meter section of a non-magnetic conductor with radius r. It also assumes the current is spread uniformly and ignores end effects. Inside the conductor, Ampere's law is used to find the magnetic field intensity H. The field is concentric and constant within the conductor. From H, the magnetic flux density B inside the wire is calculated. The...

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key terms and concepts

Learn how Ampere's law is used to find internal and external flux linkages in a solid cylindrical conductor, and how they combine to give total inductance.

Magnetic Flux Linkage in Solid Conductors | JoVE K12

JoVE Core 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Magnetic Flux Linkage in Solid Conductors

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