If there exists a natural magnetic field due to the metallic core of the earth... could we then extract and get free energy from the earth core ??


Anwering some specific details of the question - for an in-depth answer, see the duplicate Can the Earth's magnetic field be used to generate electricity?:

If we see the Earth's magnetic field as fixed, like if the Earth's core would be a big permanent magnet (it's not, see below), and we want to generate electricity while we are not moving, we have a magnetic field that does not change.
We can not extract energy from a static magnetic field like we can not do that from gravity, when not moving - there's just a force (, and some other force balancing it; that's why we do not move).

But the magnetc field of the Earth is not created by the core of the Earth in a way similar to a permanent magnet.
The related question "How is earth a magnet while it's volume is mostly above curie temperature?" has a good description in the answer of @ParthVader.

In summary, the field is created by dynamic processes, which do not happen in the "inner core" - the solid metal center of the earth, but in the more fluid outer regions of the Earth.

The interesting point is that the process that creates it is dynamic.
This means the field is not necessarily fixed.
Actually, there is some small change of the field over time;
But it's so little that we can not obtain any useful amount of electric energy from it. I'm not sure it's enough to even easily measure it experimentally.

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