$A$ long insulated copper wire is closely wound as a spiral of $N$ turns. The spiral has inner radius $a$ and outer radius $b$. The spiral lies in the $X-Y$ plane and a steady current $I$ flows through the wire. The $Z$-component of the magnetic field at the center of the spiral is

• A
  $\frac{\mu_0 N I}{2(b-a)} \ln \left(\frac{b}{a}\right)$
• B
  $\frac{\mu_0 N I}{2(b-a)} \ln \left(\frac{b+a}{b-a}\right)$
• C
  $\frac{\mu_0 N I}{2 b} \ln \left(\frac{b}{a}\right)$
• D
  $\frac{\mu_0 N I}{2 b} \ln \left(\frac{b+a}{b-a}\right)$