When teaching electromagnetism in schools, many teachers make use of an apparatus similar to this:
This got me wondering, does the mass of the iron nail affect the strength of the magnet?
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I believe this scenario would be mass independent. The strength of a solenoid's field with no core is B=unI while the strength of a solenoid with a core is B=kunI with k being a constant which is the relative permeability of the core substance. As you can see, by just adding a constant with a core, it would be mass independent.
B = Magnetic field strength (Teslas)
u = Permeability of free space (1.26*10^-6 Tm/A... I actually don't remember the rest of this unit)
n = The number of turns over the length of the wire. You will also see this written as N/L.
I = The current flowing through the wire (Amperes)
k = The relative permeability of the core substance (dimensionless)