Ferromagnetic core with air gap
You don't have enough information to calculate the H field or the flux in the gap.

You do know the available mmf (magneto motive force) which is 8amps * 200 turns = 1600 At.

The resulting H field is 1600/L, where L is the effective magnetic length.

Given that you have no information about the detailed geometry of the system (other than the lengths), you can assume that the effective air-equivalent magnetic length is 4*l = 800mm of iron, plus 1mm of air. 

To write that as a single figure, we need the permeability of the iron. The effective length is then 800mm/ur_iron + 1mm.

One common option is to assume ur is infinite, which is sort of OK for small air-gaps. This air gap is quite large, and the difference between using 'typical' values of ur, which are in the 1k to 10k range, and infinity, is quite a substantial fraction.