neodymium magnets are basically 1 million amp turns per meter, and when the magnet is in open air, the magnetic field strength inside the magnet is about 1 to 1.1 T depending on the grade. (n42 to n52)
now because the magnetic field value measured in teslas or lines of flux per square inch, follows the square root of the energy stored, when you take an average magnet, and slip it inside a completely enclosed steel box, the magnetic field strength will increase 50% to about 1.4 to 1.5T. this is actually dependent on the geometry of the magnet as well.
For various reasons this is hard to understand.
imagine an infinite grid of resistors, say 100 by 100 resistors. take a block of them, say, 2 by 6 resistors, and replace them with voltage sources in series with the existing resistor, all pointing in the same direction. then ask what's the current flowing through any individual resistor.
The further you get away from the voltage source, the less current flows.
Now take your 2 by 6 grid of voltage sources and cut down the grid of resistors, say 2 resistors away from the voltage sources, and short out all the resistors to the edges of the box.
now as you can understand, the total current increases and the voltage across any given resistor is significantly increased.
that's what happens when you surround the magnet with metal.
steel has a resistance of about 1/1000 to 1/10000th that of air. but the magnet itself is an air gap, which is why the flux density only increases 50% when the magnet is shorted out.
alnico magnets have a permeability of about 10, which is why they can be easily demagnetized. they can have a flux density change by like 5:1 when shorted out with steel iirc. (.2T in open air, 1T inside a core)
so the whole point of an iron core, is to make the magnet field value far higher with less volume of magnet that would otherwise be required.
for example, hvac fan motors are now using embedded magnets, 100 watts shaft hp can be acquired at 1250 rpm from 8 magnets 1mm thick about 1cm square.
there is a minimum volume of magnet required but it gets less and less as the magnetic path is optimized.
for air core alternators you want the volume taken up the the copper windings to be the only air gap in the system, and you want to put as much copper as is practical into that air gap, in a coil configuration that has the most turns per unit area for the least total path length of the copper winding.
