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Can light, as an electromagnetic wave, cause electromagnetic induction in a wire by passing near the wire? Does a moving electromagnetic wave cause a varying magnetic field in the region near the wire? Could light then be used to generate power by induction?

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Light rays are produced from electric fields of electrons flowing through a resistor. On the other hand, light rays disturb electric fields of electrons in a solar cell to produce electric current. Lights are concerned only with electric field. Light rays cannot be used to disturb magnetic fields directly. Radio waves (cell phone waves) are concerned only with magnetic field. Radio waves cannot be used to disturb electric fields or light rays directly.

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Note that light (in one of its interpretations) is a Electromagnetic Wave. Now, there is a huge difference between the oscillating magnetic field in an EM wave and a magnetic field generated by a permanent magnet or an electromagnet.\

One of the differences is that magnitude of the magnetic field in an EM wave happens to be very small. In fact, the magnitude of the electric field is c (speed of light) times more than the magnetic field. It is very difficult to cause induction in a wire via the magnetic field of the EM Wave.

However, as explained already by @Alex, the electric field component of an EM wave can cause electrons to oscillate in a wire.

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