You can use the following analogy
when attempting to explain the production of a voltage by the cutting of magnetic field lines.
Imagine a cornfield with the combine harvester cutting the corn stalks. The cutting is more
effective when the cutting edge is at right angles to the corn stalks. This is an analogy with
the cutting of magnetic flux by a wire - it is more effective and so generates a greater
potential when the wire is moving at right angles to the field
direction.
At
positions A the blades are cutting through the corn stalks – this corresponds to a wire cutting
through the field lines at right angles giving a large voltage.
At positions B the blades
are sliding along the corn stalks – not cutting them. This corresponds to a wire moving along
the lines of the magnetic field and not producing a voltage.
The difference between this anology and a wire in a magnetic field is that the corn stalks are cut down while the magnetic field is not destroyed. You have to imagine very fast growing stalks that grow back in place as soon as they are cut down!