Speaking real simply here,
any magnet has two poles and magnetic flux flows from one pole to the other. It makes a closed loop, just like Kirchhoff's current does.
The two poles of your electromagnet are separated by the length of your nail.
Your magnetic field has to traverse that distance through air.. and air is a terrible conductor of magnetic flux.
Reducing your air gap will give a stronger field. Try bending your nail into a horseshoe shape..
Look at hardware store magnetic door catches. They all have their poles close together for that reason.
https://www.homedecorhardware.com/h...MIkMmV9tvZ2wIVBpNpCh2AbgcDEAQYASABEgLfFPD_BwE
View attachment 227044This page addresses permanent magnet gaps, but the principle applies to your electromagnet.
https://www.kjmagnetics.com/blog.asp?p=gap-calculator
View attachment 227045
Iron is an excellent conductor of magnetic flux.
That iron yoke let's the flux flow easily around the external part of the magnetic circuit, from top of upper magnet to bottom of lower one. One of those will be a North pole and the other a South.
That way all the magnetic "push" (MMF is what we call it) is acting on the air gap, practically none gets wasted externally.
What clever mechanical construct can you come up with to minimize your air gap and put your flux where you want it ?