yes, exactly that's why its counter intuitive. when you bring a magnet close to a ferromagnetic object, does the magnet repel? NO, it attracts. Which configuration has more energy?
The energy in a changing
closed system is always less at the end position than at the start position.
It's a general rule in nature that all systems tend to evoluate towards a state of lower energy. This evolution is rendered possible by using the internal energy taken from the more energetical starting state.
A typical case is two distant magnets that attract one another, releasing the potential energy coming from their initial relative position.
Another typical case is two near magnets that repel one another, releasing the potential energy coming from their initial relative position.
If we had not the potential difference between the start and end point, we would have no cause for the system to change. This principle is so universal that a lagrangian is enough to describe a mechanical system evolution, without even to take into account the causal relations for the time evolution.
If you integrate the B*H quantity, you will find that there is more energy in the magnetic field for option 1, when the magnet has magnetized the ferromagnetic material and attracted itself to it, thus further increasing its own magnetic energy.
That's false. When a magnet magnetizes ferromagnetic material, it provides work to change the orientation of the magnetic domains. This magnetic polarization transforms the ferromagnetic material into a magnet that acts as any permanent magnet, attracts the first magnet, and both move towards one another, reducing their magnetic potential energy.
You didn't yet realized that the potential energy in a system of two distant attracting bodies is more than when they are nearer. Same thing for the gravitational energy of distant masses, or of potential energy of distant unlike charges.
It's the contrary for repelling bodies: there is more energy when they are near from one another than away.
Moreover it's extremely simple to calculate, the potential energy difference is the work done by the force between the start and end point, we just have to integrate F*dl.
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That's because you're too ignorant to understand these things yet pretend to teach others and laugh like a fool.
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Your understanding of physics is at a so low level that you are now
explaining us that there is more energy in a system after it has released its energy than before! Yes this is laughable.

Facing such an appalling stupidity, the only possible attitude is either to
xxxxxx xxxxxxx or to laugh of it, and I prefer the second possibility.
You really need to be teached but it's impossible. I'm not teaching you, it would be useless, you consider that you are all-wise and all-knowing, the last stage of the Dunning-Kruger symptom. I'm just correcting your inappropriate approximations, your misinformations, your mistakes and your nonsenses that you are regularly and pretentiously spreading on this forum and that could mislead other contributors.