Hey,
So if we look at AB, then this side is moving up.
Using your right hand. make the fingers go from North to South (Point the tips towards the South end). Now make your palm face the direction that the side is moving towards, from AB, it is moving up, so make your palm face upwards.
Now extend your thumb out and make it perpendicular to your palm, the direction it is facing is the current direction.
(Do this for side DC and you will notice the current goes from D to C)
This answer is confused because it does not point out the confusion in the author's original question. An electric current is induced in a generator, not a motor. In a motor we are converting electrical energy into mechanical energy in the form of the rotation of the armature windings. The armature rotates because there is already a current going through the loop. There is no 'induced' current.
In a
generator we do the opposite. Here we are converting mechanical energy of the rotation to electrical energy (the induced current). If this is what you are inquiring about, you should use Lenz's law. If the magnetic field is going from left to right, and the coil is rotating clockwise (all as per the above diagram), then the flux increases to the right as rotation proceeds (at least, at this instant in time).
Hence, as per Lenz's law, a current will be induced in the loop in such a direct that the flux it generates counteracts this; i.e. flux will be sent to the left. Using the right hand grip rule, we can ascertain the direction of the current as being from A to B (or, equivalently, from C to D).
The problem with the above is that you are using the Lorentz force equation where you should be using Faraday's law of induction... The above answer would be correct if the OP meant to say simply the 'current' in the windings of the motor, rather than the 'induced' current.