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

To calculate a solid cylindrical conductor&#39;s inductance, consider a 1-meter section of a non-magnetic current-carrying conductor with radius r, disregarding end effects and assuming uniform current density.
Ampere&#39;s law calculates a constant concentric magnetic field inside the conductor.
Given a uniform current distribution, the magnetic field and flux density are determined.
Then, the differential flux per unit length is computed, which determines the total flux linkages inside the conductor.
This allows the calculation of the conductor&#39;s internal inductance per unit length.
To find the magnetic field outside the conductor, Ampere&#39;s law is applied to a contour enclosing all the current. This aids in calculating magnetic flux density, differential flux, and flux linkage outside the conductor.
Integrating between two external points gives the external flux linkage and consequent external inductance per unit length.
The total flux linkage at an external point is the sum of internal and external flux linkages, which determines the total inductance.
Finally, considering an array of cylindrical conductors, each carrying a current, with their total current equaling zero, the flux linkage is calculated.

inductance: solid cylindrical conductor

Inductance: Solid Cylindrical Conductor

To calculate the inductance of a solid cylindrical conductor, consider a 1-meter section of a non-magnetic, current-carrying conductor with radius r. Disregarding end effects and assuming uniform current density, Ampere's law helps determine the magnetic field inside the conductor. This law states that the magnetic field intensity H is concentric and constant within the conductor.
Given the uniform current distribution, the magnetic field Hx and flux density Bx inside the conductor are calculated. The differential flux per unit length inside the conductor is then computed, leading to the total internal flux linkages, which derive the internal inductance per unit length.
<img alt="electrical inductance calculation formula; equation in physics; key symbols Lambda, Mu; educational" src="/files/ftp_upload/16141/16141_Equation%201.svg" style="height: 28px;" data-altupdatedat="1762173717000" data-alt="Equation1" />
To determine the magnetic field outside the conductor, Ampere's law is applied to a contour enclosing the entire current. This helps calculate the magnetic flux density and the differential flux outside the conductor. Integrating these values between two external points provides the external flux linkages and the resulting external inductance per unit length.
<img alt="Electromagnetic induction formula diagram, showing mutual inductance equation for scientific analysis." src="/files/ftp_upload/16141/16141_Equation%202.svg" style="height: 28px;" data-altupdatedat="1762173717000" data-alt="Equation2" />
The total inductance at an external point is the sum of the internal and external flux linkages. This comprehensive approach ensures an accurate determination of total inductance.
<img alt="Mutual inductance formula, \(L_P = L_{int} + L_{12} = \frac{\mu_0}{2\pi}\left(\ln\frac{D}{r} + \frac{1}{4}\right)\)." src="/files/ftp_upload/16141/16141_Equation%203.svg" style="height: 28px;" data-altupdatedat="1762173717000" data-alt="Equation3" />
When considering an array of cylindrical conductors, each carrying a current such that the total current equals zero, the flux linkage is calculated by summing the contributions from each conductor. This ensures the accurate calculation of inductance for complex conductor configurations, which is essential for optimizing the performance and efficiency of electrical systems. This method combines internal and external inductance to provide a complete understanding of the inductance in practical applications.

To calculate a solid cylindrical conductor&#39;s inductance, consider a 1-meter section of a non-magnetic current-carrying conductor with radius r, ...

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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.

Magnetic Flux Linkage in Solid Conductors

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