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I'm a freshly graduated electrical engineer. One course that I really struggled with was Field Theory, because it was a lovely assortment of vector calculus and things that were explained to me well above my level. As a result, I can design a really awesome circuit board, but I don't really understand the fundamental rules of the universe that really let me do that.

So I understand the electromagnetic spectrum -- electromagnetic radiation (EMR) is mediated by photons with energy $E = h\nu$, and so on. These photons are absorbed and emitted by atomic reactions. What I was told, or at least what I am under the impression is, that both electric and magnetic fields are also mediated by photons. This is where I get lost; I can't visualize how it works. When I hold up two magnets together, are they exchanging photons? When I close a switch, and current flows due to the existence of an electric field, where do these photons come in? I am perfectly find understanding that electrons flow under the potential gradient, I just don't see where photons come in.

I took the physics classes, which describe what goes on at the lowest level, and electrical classes that described things at a much more abstract level, but neither side really put things together, so I've got this frustrating knowledge gap.

As a corollary question: If $E = h\nu$ for photons, then how can antennas that emit a constant frequency have varying power? You see warnings about not to get too close to some high-power antennas because you'll get roasted. Is it because the quantities of photons being emitted?

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Yes to both yes/no questions, for one. –  Emilio Pisanty May 10 '13 at 1:42
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Hi @Bamako, and welcome to Physics Stackexchange! Your last paragraph is sufficiently different that I'd suggest breaking that off into a new question. (Your hunch is right by the way, but a full-fledged answer would probably prove more insightful than this lowly comment.) –  Chris White May 10 '13 at 1:42
    
There is a great book of popular lectures, Feynman: QED, The Strange Theory of Light and Matter. –  firtree May 10 '13 at 7:00
    
Possible duplicate: physics.stackexchange.com/q/3580/2451 –  Qmechanic May 10 '13 at 9:49

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So I understand the electromagnetic spectrum -- electromagnetic radiation is mediated by photons

Briefly, electromagnetic radiation is due to real (observable) photons; electric and magnetic force are due to virtual photon exchange.

The macroscopic electromagnetic wave phenomena we observe are due to an almost unimaginable number of photons, electromagnetic "quanta", coherently adding together.

This is where I get lost; I can't visualize how it works.

This topic is not something that one "groks" overnight or, if you're like me (an EE), over some period of years. It's a continuous process.

Just today, while driving to Lowe's, something I had been thinking a long time about in quantum field theory suddenly became very clear.

The fact is, no matter how many classes you take or books you read, much of the material must, like a great chili, "stew" for awhile before it's ready.

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