Considering the magnetic force on a single charge (e) we find

Now the total force on a wire comprised of (nAl) charge carriers each with charge e is given by

Defining a vector l along the wire in the same direction as J and using |JA| = i (electric current) we find for the total force on the wire

                        

  Note that for a given current negative and positive charge carriers move in opposite directions.  This leads to  a force on the wire in the same direction (see above), whether the charge carriers are positive or negative.