This problem is in reference to **Q3.239** in Problems in General Physics by I.E. Irodov.

Question: N = $2.5\*10^3 $wire turns are uniformly wound on a wooden toroidal core of very small cross-section. A current I flows through the wire. Find the ratio 1 of the magnetic induction inside the core to that at the centre of the toroid. 

Assuming an Amperian loop in the central space of toroid directly gives us B = 0 at .the center, similarly inside the toroid gives us $$ B = \mu NI / (2 \pi r) $$ and this is also what I have found in many reference books too. But the answer given is $$ \eta = N / \pi$$

Where have i missed?
Thanks.