$A$ coil having $N$ turns is wound tightly in the form of a spiral with inner and outer radii $a$ and $b$ respectively. Find the magnetic field at the centre,when a current $I$ passes through the coil.

• A
  $\frac{\mu_{0} I N}{2(b-a)} \log _{e}\left(\frac{b}{a}\right)$
• B
  $\frac{\mu_{0} I}{8}\left[\frac{a+b}{a-b}\right]$
• C
  $\frac{\mu_{0} I}{4(a-b)}\left[\frac{1}{a}-\frac{1}{b}\right]$
• D
  $\frac{\mu_{0} I}{8}\left(\frac{a-b}{a+b}\right)$