(N/A) current-carrying conductor placed in a magnetic field experiences a magnetic force. The magnitude of this force is given by $F = BIl \sin \theta$,where $B$ is the magnetic field strength,$I$ is the current,and $l$ is the length of the conductor.
$(i)$ If the current $(I)$ in rod $AB$ is increased,the magnetic force $F$ increases,leading to a greater displacement of the rod.
$(ii)$ If a stronger horse-shoe magnet is used,the magnetic field strength $(B)$ increases,which increases the magnetic force $F$,resulting in a greater displacement of the rod.
$(iii)$ If the length $(l)$ of the rod $AB$ is increased,the magnetic force $F$ increases,which also leads to a greater displacement of the rod.