Some general information on electromagnets:
As already mentioned, the magnetic strength is a function of the current in the winding, and the number of turns in the winding. The term is amp-turns. If you double the number of turns, you will have more magnetic strength with the same current. Of course, the DC current through the winding is a function of the applied voltage and the resistance, as per Ohms law.
The magnetic field, or lines of force, flow between the two open ends of the winding, beginning at the axial face of the winding. If it is an E core, then the magnetic field splits, with half of the force flowing from the center face to each of the two outside faces.
Note that I said that the magnetic field begins where the winding ends. That means that, if your winding only goes partway up the core, that some of the magnetic field goes right across the unwound length instead of going out from the ends of the core. In other words, if the winding doesn't cover the full length of the core legs, a lot of the magnetic field isn't out where it does you much good. That being said, if you are using prewound bobbins that are shorter than the length of the core legs, it is better to position the coils close to the open ends, than at the the base. That will maximize the force lines from the open end to be out in your 'working' area.
More info on the working of electomagnets can be found here: https://en.wikipedia.org/wiki/Electromagnet