[Bored chemist]

Why did you bother to post that?
The results are exactly what we would expect.

[Mitko Gorgiev (OP)]

I have uploaded an experiment video on electric generation by moving magnets through a coil.

Let us know if the result agrees with your expectation.

The explanation of Hamdani’s experiment is pretty simple. The magnetic field is strong only at the ends of the magnet, that is, at its poles. Along the length of the magnet the field is very weak. That’s why there is no current induced in the coil when the pretty long magnet is moving inside the coil.
When there is a nut between two magnets which are facing each other with the opposite poles, then the situation is not much different compared to the previous case.
Now the third case:
When there is a nut between two magnets which are facing each other with the same poles, then the induced current is considerably greater than the induced current when we are moving the magnet in or out of the coil with one of the poles ahead. Why?
Look please at the drawing below:

magnet toward a coil.png (3.25 kB . 690x220 - viewed 1882 times)
In the figure (a) the magnet is moving with its plus-pole ahead toward a coil. The induced current is flowing toward us, so to say.
In the figure (b) the magnet is moving away from the coil with its minus-pole ahead (the plus-pole is nearer the coil). But this is happening at the other side of the coil. The induced current has the same direction as in the figure (a).
Look now at this drawing:

magnet through a coil.png (2.38 kB . 360x150 - viewed 1975 times)
Two magnets with a gap between them are moving leftwards as a whole through a coil as shown in the figure. When the coil is exactly in the middle of the gap, then the induced current in it is twice as strong compared to the case when only one of the magnets is moving. It is so because we have here both cases from the figures a) and b) united in one.
The nut in the Hamdani’s experiment makes actually the gap between the magnets and at the same time keeps them together.

P.S. I call Plus the pole of compass which points North. In relation to this, please see:
Is the designation "positive" and "negative" in electricity arbitrary?
https://www.thenakedscientists.com/forum/index.php?topic=78171.0

[hamdani yusuf]

The explanation of Hamdani’s experiment is pretty simple. The magnetic field is strong only at the ends of the magnet, that is, at its poles. Along the length of the magnet the field is very weak. That’s why there is no current induced in the coil when the pretty long magnet is moving inside the coil.

My explanation is that when the coil is around the middle of magnet array, the action of magnets above the coil is canceled by the magnets below it. When the coil is around the end of magnet array, the action by those magnets is not canceled. When there are two magnet arrays in opposite directions, the actions are doubled.
The iron nut is merely meant to make two magnets with same poles stick together, cancelling the repelling magnetic force. It can be replaced by a non-magnetic object glued to both magnets.

[Hayseed]

The question that you are asking is not answered with an induction loop.  It was answered and measured by Ampere.  Using force on square loops at different angles.

Angle.    The first relativity.     Then came velocity.