What is an electric field, really?

[rockyshephear]

I've been told over and over its the amount of something entering a given surface. But the amount of what? Twinkies, photons, quarks, alabaster pigs? What precisely? And if the field is really continuous and infinite, what enters can never be but one quality. It can never be greater or lesser because at every point in space is the same thing entering the surface. So what makes an electric field different to cause differing measurements of electric field?

 

[maverick_starstrider]

? Wasn't there just a topic on this? Classically an electric field can be seen as a mathematical construction of force/charge, or else it can be considered its own entity. It's really just a matter of convenience. In classical EM it is continuous but I'm not sure I understand what you mean by infinite. Do you mean it extends forever? Well it propogates outwards at c forever, yes. Do you mean its value is infinite? Then no except for certain non-physical cases (like point charges).

What do you mean "it can never be greater or lesser"? The fact that the flux is just the contained charge is actually 100% a MATHEMATICAL result of the fact that we have a spherical force and was derived with no actual mention to physics (it's just the divergence theorem of vector calculus). "What enters can never be but one quality (I assume you mean quantity)", again I don't know what you're saying here. E is a VECTOR FIELD, it is continuous in both position and intensity, classically there is no discreteness to the EM field (classically). The mechanics of classical EM are identical to the mechanics of fluid dynamics (that is actually where they came from). So if you want to think of an analogy, the E field is like the flow of water (when we approximate water to a continuous quantity just like we do with classical EM).

Quantum mechanically the E-field is discretized which leads to all sorts of fun like the Casimir effect. I don't actually know a whole lot of QED but I'm not sure if there's actually a mathematical difference in seeing the field as propogating via virtual photons or a discretized waveform. And in physics if there is no mathematical difference (i.e. we could never do an experiment to distinguish between the two) then it's really a matter of personal preference of how you want to visualize it.

 

[rockyshephear]

So saying "it's the number of flux lines that enter a surface perpendicularly" is not correct since you can't count the flux lines in the first place. You must agree this is not well stated.

 

[maverick_starstrider]

You're right,:

"it's the number of flux lines that enter a surface perpendicularly"QUOTE]

Isn't ideally stated, BECAUSE THAT'S NOT THE DIVERGENCE THEOREM. \iiint\limits_V\left(\nabla\cdot\mathbf{F}\right)dV=\iint\limits_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf F\;\cdot\mathbf n\,{d}S is. You can find its proof in any basic vector calc book. Enough with this trying to reduce things to word problems crap, if you want to learn it, learn the math. If you don't want to learn it then stop clogging up the forum with this stuff. You absolutely will not be able to do any EM unless you learn yourself some vector calc.

 

[rockyshephear]

I have been studying vector calculus but oddly I never hear anyone talking about the angle of two vectors to each other or the curl vs the paralleliped volume. Where's all this vector calculus nomenclature?