How do we know that a wave of light has electric field? Maxwell proved that light is an electromagnetic wave. Can you give me a reference of an experiment which proves light as an EM wave?
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The development is actually the other way around. We knew about light first, and only later discovered radio waves and demonstrated their similarities to light.
Obviously, we were aware of light (at least in a general way) since pre-historic time since we could see things, it was easier to see things at night if we lit a fire, etc. Later we knew we could separate light into its component colors using a prism, etc. By the 18th century we had measured the speed of light to a reasonable degree of accuracy.
But we didn't know the underlying nature of light. Both wave and particle ("corpuscular") theories of light were proposed.
In 1861 James Clerk Maxwell theoretically developed his well-known equations describing electromagnetic wave behavior. This theory predicted that electric field disturbances would propagate at the same speed as light. This theory suggested that light and electromagnetism were the same phenomenon but hadn't been experimentally proven yet.
In 1887, Heinrich Hertz performed a series of experiments to test the hypothesis that electromagnetic waves could be produced and would propagate like light. In one example, he used a spark gap to generate a disturbance of the electromagnetic field, and showed that this could be received by what we'd now call a loop antenna at some distance away from the transmitter. Hertz was also able to generate standing waves by reflecting a transmitted signal off of a sheet of metal, and from the observed standing wave pattern show that the speed of the electromagnetic wave was the same as the speed of light.
Since then, continued experimental results have all been consistent with the conclusion that light and electromagnetism are one and the same phenomenon, and none have shown any inconsistency in this theory.
In comments you mentioned,
the particle that carries that energy is known as photons. But it has no charge, so the question arises in my mind is, how can wave of light has electric field?
The charge is the source of electromagnetic waves. That doesn't mean that electromagnetic waves must carry charge. The electromagnetic wave (or the photon) is the mechanism by which a charge in one location can affect the behavior of a charge some distance away. But it doesn't have to carry the charge over to the other place and whack the 2nd charge with the first one to do that.
The Photon
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