B at center of loop vs. for wire

[SaintJude]

Has anyone noticed that the magnetic field for a long current-carrying wire is different at its center ?

Magnetic field for a long wire is:

But the magnetic field at the center of the loop is

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[BB8730]

I'll come out of lurking to make my first post because I have an exam on this material on Monday. 🙂

I think what you're asking is: if you have a long wire whose magnetic field is given by the first equation, why is it different when it turns into a loop? All other things equal and if the number of loops is 1, the only difference between the two is the extra pi in the denominator of the wire equation. I would imagine this is because in a loop, the magnetic field is coming from 360 degrees and in the wire it's only coming from one direction. Thus, the strength of the magnetic field is greater in the middle of a loop with radius=r compared to the magnetic field generated by a wire at radius=r.