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?