I am trying to study the influence on the magnetic field B generated by a solenoid in two different cases
- the solenoid is wound around an open iron core
- the solenoid is wound around a closed iron core
I am trying to use amperes law to give an estimation of the magnetic field in both cases, but I seem to arrive at a contradiction: acc to the calculation, the magnetic field with an open iron core would be bigger than that of a closed iron core. I am pretty sure this is wrong, because the flux lines in an open iron core need to travel a large distance through the air (which has low permeability), where as the flux lines in a closed iron core can travel through the highly permeable material all the time, and never need to travel in the air.
See the attached picture for my calculation. (I am assuming the coil diameter, wire diameter, number of windings, current and core material to be the same in both cases. The only difference is the iron core being open or closed)
What am I doing wrong here?