Mutual Inductance: Solving with Ampere's Law

[Frillth]

Homework Statement

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?

 

[LowlyPion]

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

 

[Frillth]

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?

 

[Redbelly98]

What's the B-field of a long straight wire?