Mutual Inductance: Solving with Ampere's Law

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Homework Help Overview

The discussion revolves around the concept of mutual inductance and the application of Ampere's Law and the Biot-Savart Law in calculating magnetic flux. Participants are exploring how to relate these concepts to find mutual inductance in a circuit setup.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formula Φ = M*I and the need to find magnetic flux due to current in a circuit. Questions arise about the applicability of Ampere's Law versus the Biot-Savart Law for this problem. There is also consideration of using integrals to calculate contributions from different points along the wires.

Discussion Status

The discussion is active, with participants sharing their attempts and questioning the best approach to use. Some guidance has been offered regarding the integration process required for calculating contributions to the magnetic field, but no consensus has been reached on the preferred method.

Contextual Notes

Participants express uncertainty about their understanding of Ampere's Law and its application in this context, indicating a potential gap in foundational knowledge that may affect their problem-solving approach.

Frillth
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Homework Statement



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Homework Equations



Φ = M*I
Biot-Savart law
Ampere's law

The Attempt at a Solution



I have the formula Φ = M*I, which means that to find the mutual inductance I simply need to find the magnetic flux through the top circuit due to the current in the bottom circuit. However, I don't yet have a solid grasp of Ampere's law. Is there a way to use Ampere's law in this situation, or am I going to have to grind it out with Biot-Savart?
 
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Frillth said:
I have the formula Φ = M*I, which means that to find the mutual inductance I simply need to find the magnetic flux through the top circuit due to the current in the bottom circuit. However, I don't yet have a solid grasp of Ampere's law. Is there a way to use Ampere's law in this situation, or am I going to have to grind it out with Biot-Savart?

Looks like you will have a double integral for each point along the second wire for all the contribution from points on the first, then integrated over its own length.

See also:
http://en.wikipedia.org/wiki/Inductance#Mutual_inductance
 
Can I use Biot-Savart to find the magnetic field at some general point (x,y) in the plane, then integrate that over the area of the top loop to get flux?
 
What's the B-field of a long straight wire?
 

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