A long insulated copper wire is closely wound asa 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

$$\frac{\mu_0NI}{2(b-a)}\ln \left(\frac{b}{a}\right)$$

B

$$\frac{\mu_0NI}{2(b-a)}\ln \left(\frac{b+a}{b-a}\right)$$

C

$$\frac{\mu_0NI}{2b}\ln \left(\frac{b}{a}\right)$$

D

$$\frac{\mu_0NI}{2b}\ln \left(\frac{b+a}{b-a}\right)$$