Does this help: http://www.tutorvista.com/content/physics/physics-iv/moving-charges-magnetism/lorentz-force.php
Update: Sorry, I misread one of the symbols. The conclusion is that the force is L*(I cross B) where L is the length of the wire segment, I is the current vector and B is the magnetic field vector.
The assumption is that the magnetic field is constant over the length of the wire segment.
Here's another explanation of the same experiment: http://www.nikhef.nl/~h73/kn1c/praktikum/phywe/LEP/Experim/4_1_06.pdf with the same formula.