The figure shows a rectangular wire loop, around which a current I flows, and and an infinite straight wire. The wire lies in the plane of the loop and is parallel to, and a distance d from, the side AB. (see attachment)
Show that the amount of magnetic flux generated by the loop which links the straight wire is equal to:
Hint: Use the fact that M12 = M21 implies that Phi12 = Phi21 if the same current I flows in both circuits.
Ampère's law: int(B.dl) = mu(0)*I
Phi = int(B.dA)
The Attempt at a Solution
I've done some work on this problem and actually solved it, but all based on the following assumption:
The current flowing in the wire is equal to the current flowing in the loop.
Because then you can calculate B that is generated by the wire and the effect it has on the loop using Ampère's law. Phi is then just the solution of the equation above, with the integration limits of d to d+l.
This gives the right solution, but is it correct to assume this? I cannot do it the other way round, i.e. calculate the B-field generated by the rectangular loop; what would dl be in this case? And also dA for the following equation?
Any help or hints would be greatly appreciated!