When a current carrying wire is in a magnetic field a force is exerted on the wire:

F = iL x B

where F,L and B are all vectors.

The main point, here, is that these three vectors are all at right angles to one another, as represented by the "cross product" (Right Hand Rule). If the magnetic field is pointing down and the current (positive charges) runs left to right the force will be toward the "rear", as in the photo . If you reverse the direction of the current, the force on the wire will be toward the "front". This is shown nicely by the demonstration apparatus we used. A power supply provides about 20 Amperes of current and the wire is hinged at the top of the support. A strong magnet provides a field from top to bottom.