Calculating the magnetic field inside a closed loop of wire

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A closed loop of wire carrying a clockwise current generates a magnetic field at its center, which can be calculated using the Biot-Savart Law. The user successfully applied this law to find the magnetic field but encountered confusion when using Ampere's Law, as the enclosed current was zero, suggesting no magnetic field. However, it is clarified that the absence of enclosed current does not imply a zero magnetic field; rather, it indicates no net field along the direction of the amperian loop. The discussion emphasizes the importance of understanding the distinction between enclosed current and the presence of a magnetic field. Ultimately, the magnetic field's direction at the center of the loop must be determined despite the zero enclosed current.
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Homework Statement



I basically have a closed loop of wire with a current flowing through it clockwise. I need to determine the magnetic field in the center, along the z-axis.

Homework Equations



Ampere's Law and Biot-Savart Law

The Attempt at a Solution



Using Biot-Savart Law I actually pretty easily calculated the field and it was correct. (sorry for not typing out formulas but the math symbols seem to be giving me trouble and I don't think I need to).

But if I use Ampere's law, then as soon as I place an amperean loop in the middle of the wire the I enclosed is 0, leading me to believe there should be no magnetic field within the wire. How am I using Ampere's law wrong?
 
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What direction is the magnetic field going at the center of the wire-loop?
And just because there's no current enclosed doesn't mean there's no magnetic field... just no net field along (and in the direction of) the amperian loop.
 

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