Does stacking two magnets together increase the magnetic strength? Just wondering if adding two (or more) identical magnets together increases their magnetic strength (in Tesla) as I am doing a physics write-up on the Lorentz force (Fleming's left-hand rule) as I tried stacking magnets together but found that the force produced is still the same. Wondering if I'm doing anything wrong.
 A: Yes, stacking magnets does increase the field, but not always by a lot---it depends on the physical arrangement.
For your first test, make a small spacer and put two magnets one on top of the other on either side of this spacer. The field between the two magnets will be strong, approximately twice that of either magnet on its own.
Next put two magnets next to each other, with N poles in the same direction. Now you have roughly the same magnetic field at the end of either magnet as you would get using a single magnet, but notice that this field is now available over a wider region.
Finally, with one magnet stacked on top of another, look at the field at either end of the pair. Now the field is a little bigger than that of a single magnet, but not much (unless the magnets are wide and flat). The reason is that the field from each magnet on its own is reducing in strength quite quickly as you move away from that magnet,
so when they are stacked this way you are not adding two fields at their full strength, but rather the full strength of one is added to a field at one magnet's length away from the other, and this second contribution is smaller.
I won't tell you all the answers here but you might like to learn a bit more about how quickly the field falls in strength as you move away from any given magnet. The field is approximately (but not precisely) that of a dipole. You could make a crude measurement of the field strength by using a small test magnet on the end of a non-magnetic spring, and using Hooke's law for the force from the spring.
A: Assuming that the field from one magnet does not effect the magnetization of the other, then the resultant field at each point will be the vector sum of the two separate fields.  That in tern depends on the position and orientation of the two (as described by Andrew Steane).
