Electromagnet flux density calculation knowing specs of coil, core and applied voltage?
I am not sure that this model is practical as the coil would be a single layer of 42 awg wire (7.06e-5 meters dia. compared to the iron core of 30mm) and the mmf is about only 20 amp-turns. The flux density in the core is a maximum of .009 tesla at the od and .003 near the center. The field is a maximum of .005 tesla very near the core but diminishes rapidly away from the core. 

I modeled this in Finite Element Analisys (FEA) software. I don't know of a reliable equation for solving this inductor because the flux densities vary widely depending upon location in the core or field.  Incidently, 0.2 amps is too high to run in 42 awg wire continuously.