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

为计算实心圆柱导体的电感，需考虑一段长度为1米、半径为r的非磁性载流导体，忽略端部效应，并假设电流密度均匀。
安培环路定律计算导体内部恒定的同心磁场。
在电流分布均匀的情况下，可确定磁场和磁通密度。
然后计算单位长度的差动磁通量，以确定导体内部的总磁通链。
这允许计算导体单位长度的内电感。
为了求解导体外部的磁场，将安培环路定律应用于包围全部电流的闭合回路。这有助于计算导体外部的磁通密度、微分磁通以及磁通链。
在两个外部点之间进行积分可得到单位长度的外部磁通链以及相应的外部电感。
外部一点的总磁链是内磁链和外磁链之和，该值决定了总电感。
最后，考虑一组圆柱形导体，每个导体均载有电流，且它们的总电流等于零，此时可计算其磁通链。

电感:实心圆柱导体

Inductance: Solid Cylindrical Conductor

要计算实心圆柱形导体的电感，请考虑一段半径为 r 的非磁性载流导体，长度为 1 米。忽略端部效应并假设电流密度均匀，安培定律有助于确定导体内部的磁场。该定律指出，磁场强度 H 在导体内是同心且恒定的。
给定均匀电流分布，计算导体内部的磁场 H_x 和磁通密度 B_x。然后计算导体内部每单位长度的差分磁通，得出总内部磁通链，从而得出每单位长度的内部电感。
<img alt="Equation1" src="/files/ftp_upload/16141/16141_Equation%201.svg" style="height: 28px;">
为了确定导体外部的磁场，将安培定律应用于包围整个电流的轮廓。这有助于计算导体外部的磁通密度和差分磁通。将这些值在两个外部点之间积分可得出外部磁通链和由此产生的每单位长度的外部电感。
<img alt="Equation2" src="/files/ftp_upload/16141/16141_Equation%202.svg" style="height: 28px;">
外部点的总电感是内部和外部磁通链的总和。这种综合方法可确保准确测定总电感。
<img alt="Equation3" src="/files/ftp_upload/16141/16141_Equation%203.svg" style="height: 28px;">
当考虑一组圆柱形导体时，每个导体都承载着电流，使得总电流等于零，磁通链是通过对每个导体的贡献求和来计算的。这确保了复杂导体配置的电感的准确计算，对于优化电气系统的性能和效率至关重要。该方法结合了内部和外部电感，可以全面了解实际应用中的电感。

计算实心圆柱导体的电感时，考虑一段长度为1米、半径为r的非磁性载流导体，……

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Transmission Line Parameters

传输线参数

KEY TERMS AND CONCEPTS

关键术语与概念

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.

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JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Magnetic Flux Linkage in Solid Conductors

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