What is Fermi surface? Fermi surface in Fermi Gas model is a sphere. Limiting objects in 1dim, 2dim, 3dim.
Why is the area arround Fermi energy, i.e. the limit, important? Because only electrons in those states can change state due to thermal and other influences (the deep inside electrons have nowhere to go, all occupied). Electric and magnetic phenomena, Lorentz force.

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