Well I think when motion is produced by a current in a conduct, we use Flemings Left Hand rule to predict the direction of motion. Whereas, when motion is producing current we use FLEMINGS RIGHT HAND RULE. It’s same as Flemings Left Hand rule but this time you do it with your right hand to predict the direction of induced emf or current. In this case the thumb will show the direction of motion, forefinger will show the direction of magnetic field and the middle finger will show the direction of the induced emf or current.
The left hand rule is a very simple rule to apply -
1) Stretch out the thumb , first finger and the middle finger (!!) such that they are mutually perpendicular.
2) If the middle finger is pointing towards the direction of flow of current(I) , then the first finger shows you the direction of the Magnetic field (B) and the thumb gives you the direction of the force experienced on the conuctor.
While applying , make sure you take 2 fingers in the same plane , the third one shall automatically give you the direction in terms of UPWARDS OR DOWNWARDS.
This rule is basically used for determining direction of the quantities and not the magnitude.
The Right hand rule also is applied in a similar way , the diff. is that the thumb gives you the direction of flow of induced current.