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As I know from Lenz's law, I can induce current in a coil just by changing the magnetic field flux inside the coil.

As I know from physics course, photons are electromagnetic waves (so they are the flux change by definition(I think)).

So if I get very small (how small?) coil and illuminate it, would I induce current in this coil? And if I got an array (how big?) of such coils, could it be useful in energetic?

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Lenz's law (for pedantics: Faraday-Henry-Lenz, IIRC Lenz's contribution was the sign) says that a change of magnetic flux induces a current. Magnetic flux is the integral of the magnetic field across a surface.

A semi-classical view of a photon is a pair of transversal electric and magnetic fields. If you shoot a photon straight through your coil, the integrand is $\vec B \cdot \hat n = 0$, where $\hat n$ is the normal to your surface, and they are 0 because of perpendicularity.

You can then decide to sacrifice some surface and shoot them at an angle. They are no longer perpendicular, and so their product, albeit small, is non zero. If you have many photons that do not come from a laser, they will be out of sync, and where one of them has a positive $\vec B$, some other will be negative, and they cancel out.

If you shoot them one by one, you are pushing the limits of the semi-classical approximation. Assuming it were valid, yes, the integral would be non zero, and induce a small current. If you are shooting a red photon, in $10^{-12} s$ it will change directions, and then you will register a negative current, so they cancel out.

You may think now that noting is stopping us from using longer wavelengths, where the frequency is low enough so we can actually measure it. Well, then, you have one of these, a loop antenna:

A coil

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