Final answer:
The magnitude of the current flowing in the 5-turn loop is 5 A, as it must create an opposing magnetic field equal to that of the infinitely long wire carrying 25 A to result in zero magnetic field at the center of the loop.
Step-by-step explanation:
The student's question is about finding the magnitude of current flowing in a 5-turn circular loop located in the x–y plane, given that there is an infinitely long wire carrying a 25-A current in the positive x-direction placed along the x-axis. Assuming the magnetic field created by this wire and the loop's magnetic field cancel each other at the loop's center (since the field is zero there), we must find the current in the loop that would create such a scenario.
According to Ampere's Law and the Biot-Savart Law, the magnetic field at a distance r from an infinite, straight wire with current I is given by B = (μ0 • I) / (2 π • r).
For the field at the center of the loop to be zero, the loop must create an equally strong but opposite magnetic field to that of the straight wire. Since the loop has 5 turns, the net magnetic field would be 5 times that of a single turn at the same distance from the wire.
Therefore, to create a magnetic field opposite to that of the wire,
the loop would need a current Iloop such that 5 • Bloop equals Bwire.
Solving this with the provided current on the wire, we find that the magnitude of the current flowing in the loop is 5 A.