the left hand rule, known as Fleming's left hand rule, is used to predict the motion of a wire carrying current when the wire is placed in a magnetic field. As you know, the current in the wire will induce a magnetic field and that magnetic field will react with the magnetic field of the magnet. the left hand rule helps you predict the movement of the wire.
Point your thumb straight out, and use your first finger to point in the direction of the magnetic field, and your second finger in the direction of the current. Your thumb will be pointing in the direction of the force experienced by the wire.
Can someone explain me the left-hand rule in Electrodynamics?
Yes,how about aplying the definition?
[tex]\vec{F_{em}}=I\vec{B}\times \vec{l}[/tex]
where [itex]\vec{l}[/itex] has the sense of the current.
Accidents may happen and people may lose their fingers...The cross product may be forgotten...But,hey,Fleming's stupid rule may be forgotten as well.