Apiece of wire is bent to form a circle with radius r. it has a steady current i flowing through it in a counterclockwise direction as seen from the top (looking in the negative z-direction).
what is bz(0), the z component of b at the center (i. e., x=y=z=0) of the loop?
express your answer in terms of i, r, and constants like μ0 and π.

B=μ₀I/2r

Explanation:

Produced magnetic field due to an existing electric field through a coil or conductor can be explained by Biot-Savart Law. Formula for this law is:

dB=(μ₀I/4π.r²)dL

Here,

r=Radius of the loop

I and r are constants with respect to length L.

To convert linear displacement L into angular displacement Ф:

dL=r.dФ

So,

dB=(μ₀I/4π.r²)r.dФ

dB=(μ₀I/4π.r)dФ

Integrating both sides over the circle i.e. from 0 radians to 2π radians  (360⁰), while the integration will apply only on dФ as all others are constants.

B=(μ₀I/4πr)(2π-0)

B=(μ₀I/2r)

correct it is c.) b b