I've always thought that a magnetic field must cross the wire to induce any change in it. But now I've learned that it actually doesn't have to even touch it, since the induced voltage in it is only dependent on the rate of change of magnetic field inside the loop of wire (doesn't matter if that field is actually changing inside the wires of the loop).
How is it that magnetic field that isn't even touching the wires induces a voltage inside of them? How does the wire "know" what the amplitude of magnetic field is in a space where there is no wire? This is beyond bizarre.