Question

how to select a direction for the EMF included In a moving conductor?

Answer 1

The direction of EMF included in a  moving conductor is determined by the right hand rule.

Loop according to a right-hand rule (point thump in positive direction of the area vector; finger then point in positive direction of the emf). then tells the direction of the induced emf.

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Answer 2

Fleming's right-hand rule (for generators) shows the direction of induced current when a conductor moves in a magnetic field. It can be used to determine the direction of current in a generator's windings.

When a conductor such as a wire attached to a circuit moves through a magnetic field, an electric current is induced in the wire due to Faraday's law of induction. The current in the wire can have two possible directions. Fleming's right-hand rule gives which direction the current flows

The right hand is held with the thumb, first finger and second finger mutually perpendicular to each other (at right angles.

The thumb is pointed in the direction of motion of the conductor.

The first finger is pointed in the direction of the magnetic field. (north to south)

Then the second finger represents the direction of the induced or generated current (the direction of the induced current will be the direction of conventional current; from positive to negative).