Magnetic flux through a rectangular loop inside a wire

[D Nguyen]

Homework Statement

Homework Equations

Magnetic flux = integral(B dot dA)
line integral(B dot ds) = (u_o)(i_enc) (Ampere's Law)

The Attempt at a Solution

I can't see how Ampere's law applies because all of the magnetic field vectors along the loop will be perpendicular to that stretch of loop. The best solution I can think of is to divide the cross section of the wire into infinitesimal pieces and see how much flux through the loop each piece contributes. However, this seem very impractical and I feel like there's a more elegant approach to the problem. Please help me figure out where to start.

 

[kuruman]

Use Ampere's Law to find magnetic field as a function of y, the distance from the axis of the wire. Use this to find the flux through a strip dy of length x located at y on the given rectangular loop. Integrate.