you use fleming left hand rule when there is a current given(eg
presence of a battery) to find force.
direction of your middle finger is direction of a proton beam.
that means, if they give u an electron beam moving to the right, u
have to reverse the direction and point your middle finger to the
left. (proton flow is opposite direction to flow of electrons, like
your conventional and non conventional current flow idea.)
index finger points from north to south(magnetic field). use it
for stuff like dc motors where u have a battery to drive the motor.
then the direction your thumb points will be the direction of force
on the conductor.
you use fleming right hand rule when there is a force given but
you are asked to find induced current(in this case, no battery to
drive the circuit). same as above, index finger points from
north to south(magnetic field), point your thumb in the direction
of the force. the direction where your middle finger point will be
the direction of the proton beam. if they wan direction of electron
flow jus reverse the direction....
use right hand rule for stuff like ac motors.
hope it helps.