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Textbooks just seem to utter that change in the magnetic flux that is 'piercing' the plane contributes to electricity induction. They don't explain why.

Is there any intuitive explanation?

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    $\begingroup$ "Why?" is a hard question to answer. When physicists explain something in response to "Why?" it always comes down to an explanation in terms of some theory. But at the root of any theory are axioms that go unexplained. Can you explain why $F=ma$? In the case of electricity and magnetism, the unexplained axioms are Maxwell's equations. The justification is that the logical consequences of the axioms accurately describe what's observed in nature. Another way of approaching your question is to ask you: What do you accept as true so that we can use it as a starting point for an answer. $\endgroup$ – garyp Jul 29 '16 at 1:29
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    $\begingroup$ To extend @garyp thoughts, the underlying theory that explains this fact is pretty dense compared to the kind of E&M that is presented in a introductory book. This is one you have to simply accept as experimentally backed gospel for a couple of years until you are ready to apply a Lorentz transformation to a second rank tensor in a Minkowski space. $\endgroup$ – dmckee Jul 29 '16 at 3:15
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    $\begingroup$ @dmckee: After which everybody will (hopefully) understand how the second rank tensors were derived from a century's worth of experiments with wires and magnets, light sources, mirrors, lenses and other contraptions. And those who don't will have a huge gap in their physics education, which I would find very sad. $\endgroup$ – CuriousOne Jul 29 '16 at 8:23

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