Mutual Inductance: Solving with Ampere's Law

AI Thread Summary
To solve for mutual inductance using Ampere's Law, one must calculate the magnetic flux through one circuit due to the current in another. The formula Φ = M*I indicates that mutual inductance is directly related to the magnetic flux. While Ampere's Law can be applied, it may require complex double integrals to account for contributions from each point along the wires. Alternatively, the Biot-Savart Law can be used to find the magnetic field at a point and then integrate over the area of the top loop to determine the flux. Understanding both methods is essential for effectively solving mutual inductance problems.
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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