# What is an electric field?

1. Jul 28, 2009

### rockyshephear

What is an electric field???

If you have just one point charge of 1 Coulomb in the entire universe, and you look at the magnetic field at a foot away vs a mile away, I maintain there is no difference that anyone can explain. Sure the equations say there's a difference but to me, it's an infinite field and as such, what creates the difference in field? Certainly not the distance between waves since it's infinitely small. Is it like electronics amplitude. So an inch away the amplitude in an inch tall but a mile away the amplitude is much less? Or is it because of some magical thing that no one understands and the only way we see it and describe it is because of it's affect on what's place at these points in the field?
Please don't bother answering with equations. I've seen enough. I would like an explanation in words please.
I believe no one knows what a field is. They know how to describe it, how it interacts on other matter but not why and how?
Correct me if I am wrong.

2. Jul 29, 2009

### Born2bwire

Re: What is an electric field???

The electric field is the electric force per charge.

If the field was uniform, then that would imply infinite energy.

3. Jul 29, 2009

### rockyshephear

Re: What is an electric field???

So if I said the electric force per charge were the same 1 inch away from the charge as 1 mile away. You would disagree. But you never even described the electric force as a function of distance from the point charge. So how is that description complete?

4. Jul 29, 2009

### AUMathTutor

Re: What is an electric field???

It is complete if you know what the electric force is.

Electric force: a force caused by electric (charge related) effects.

Charge: property of things affected by proportions of electrons and protons in its makeup.
Force: Something tending to cause an object not to move in uniform rectilinear motion.

Electrons and Protons: etc.
Motion: etc.

5. Jul 29, 2009

### rockyshephear

Re: What is an electric field???

Does a quantum physics guy understand what is the nature of the repelling force of two positive point charges? Would he say something like...
"It's the point charges exchanging photons back and forth so fast it acts like a kind of virtual spring, the closer you get the more compressed it is"?

6. Jul 30, 2009

### AUMathTutor

Re: What is an electric field???

My understanding is that photons are not involved at all. I think, basically, that the field just exists in space and can propagate at the speed of light, but it's the field that interacts with other particles, that is, the particles don't see each other, just the fields.

Maybe I'm misunderstanding what you're asking.

7. Jul 30, 2009

### dx

Re: What is an electric field???

Our most fundamental description of the interaction of charged particles does involve exchange of photons, but don't try to interpret/visualize this in a classical way; ''exchange of photon'' is a quantum mechanical idea, and it would be useless to try and think of it as a 'virtual spring' or anything else like that.

8. Jul 30, 2009

### rockyshephear

Re: What is an electric field???

Can you elaborate even slightly on how exchange of photons cannot be understood in a physical way. I saw in a documentary on quantum mechanics a demonstration of how exchange of some particle was an explanation for the strong for or weak force, can't remember. But the narrator was split into two scenes and he threw an illuminated ball back and forth, the faster thrown the more the guy was brought close to himself. This type of demonstration was deemed useful for the documentary.

9. Jul 30, 2009

### dx

Re: What is an electric field???

By "physical way", do you mean "classically and without mathematics"?

Unfortunately the quantum mechanical process of exchange of photons is nothing like throwing an illuminated ball back and forth. Like I said, no classical picture like that can represent the quantum mechanical process.

10. Jul 30, 2009

### rockyshephear

Re: What is an electric field???

Yes, without mathematics. I would guess that what holds two protons together in a nucleus and prevents them from pummeling out of the nucleus is a force that act locally between the two protons for instance. So one should be able to come up with some type of analogy "woops, there I go with that bad word again, lol" to give a kind of general idea what's going on. No?

11. Jul 30, 2009

### rockyshephear

Re: What is an electric field???

Oh crap. I'm talking to the guy with the fractal and just realized it. You don't care for analogies, I remember.

12. Jul 30, 2009

### dx

Re: What is an electric field???

If you want a general idea of what's going on, read "QED: The Strange Theory of Light and Matter" by Richard Feynman.

13. Jul 31, 2009

### jmb

Re: What is an electric field???

OK, I'm going to have a bash at answering your original question. But first I just wanted to add some generalities to this discussion...

It is really important to remember that physics is not a set of universal truths, or strangely magical rules. The physics we know today has been painstakingly assembled by people who have made careful observations (experiments), from which they have tried to conjecture rules (hypotheses) which they have then tested with further experiments. Those hypotheses that did not hold up to this testing were thrown out or refined until a set of working hypotheses were reached that seemed to agree with all experiments.

Some of these hypotheses have now been tested so many times and used successfully to predict events on so many occasions that they have been elevated to the status of theorems (e.g. Newton's laws). But it is important to remember that even then, these theorems are not truth. Rather they provide an extremely useful way of thinking about the processes they relate to. Sometimes the theorems appear really bizarre to us (e.g. wave-particle duality), but it has to be remembered that they aren't the ultimate truth --- they are just the best way our own minds can currently formulate the behaviour we have observed.

Sometimes also, situations are found where the theorems don't work. When looking at extremely fast speeds Newton's laws break down and must be replaced by the framework of relativity. At extremely small distances and masses they must be replaced by the laws of quantum mechanics, and some physicists believe that they also break down at extremely large distances and formulate theories based on this to explain the apparent measurements of a cosmological constant. But that doesn't mean that Newton's laws become worthless. In the vast majority of real-world situations they are still absolutely applicable and they represent an extremely useful and insight-producing way of looking at things. Bridges are built using them, and safe loading of dynamic structures determined from them.

When people first started to do experiments in electrostatics, a very useful hypothesis arose: namely that if you have a point charge at some position then the force it produces on another point charge will be proportional to the reciprocal of the squared distance between them. This hypothesis seemed to hold up well to all experiments and became known as Coulomb's Law (today it can be derived as a consequence of the Maxwell equations).

To physicists this is an extremely interesting relation, because something that decays at this rate ($\propto 1/r^2$), behaves like the physical emission of something. For instance if I have a fountain than emits water equally in all directions (ignore gravity for now) then the amount of water hitting me is proportional to the reciprocal of my squared distance from the fountain. Similarly the amount of sunlight falling per unit area on a planet is proportional to the reciprocal of the squared distance of the planet from the Sun.

It is because of this relation that we can draw imaginary 'field lines' coming out from the point charge: no matter how many straight lines I draw coming out of a single point, the density of these lines will always decrease with the reciprocal of the squared distance from that point --- thus it is a useful device to help me visualise the strength of force a test particle would feel at different positions without having to do the maths.

The question obviously arose though: what is this substance/effect that is causing the force between charges and that appears to follow this very physical decay law. This is today what we call the electric field. At the time (in fact even before the discovery of the $1/r^2$ law) the electric field was actually thought of as some kind of fluid (interestingly many electrostatics problems have identical solutions to similar hydrostatics problems, so this idea is not entirely without merit!). But since then we have discovered that it can exist entirely in vacuum and that it has many properties that are definitely unfluid like.

It is tempting then (and in simple problems even useful) to think of the electric field just as a mathematical device to 'encode' the action at a distance caused by the attraction and repulsion of charges: just as in Newtonian gravity the gravitational field is used to encode the action at a distance caused by the interactions between gravitational masses. In fact Wheeler and Feynman did consider trying to encode physics in terms of the principal of action at a distance rather than fields (although they found fields so useful in modern physics that they let the idea fall by the wayside). However this alternate way of looking at things is not necessarily any more satisfying: it leaves one with questions such as how do the objects know of each others' presence, etc.

If one does choose to describe electromagnetics using a field framework, something very interesting happens. One discovers that the logical (i.e. following from the mathematics) conclusion of setting the problem up this way is that the field itself can actually possess energy, and that changes can only propagate through the field at the speed of light. In short the field appears to actually be the mediator of the force between the two particles. It seems to have some kind of true physical existence.

Now as I've said, this all arises from a particular way of thinking about things. There may of course be other ways to formulate electromagnetism (just at there are different ways to formulate quantum mechanics). But this way of thinking about things has proved to be extremely productive. Given that, it is also a very useful exercise to try and understand the concepts behind it. Consider again Newton's laws: we know these are not the ultimate truth because they break down at very high velocities, but nevertheless the concepts they lead to (equal and opposite forces, etc) are extremely useful tools to help us understand what a system is going to do. Thus too it is extremely useful to understand the nature of the field, as bizarre and unintuitive as it may sometimes seem.

It is often all too easy when doing physics to lose track of the underlying questions ("But what is an electron?", "What is inertia?", etc.), and you are right that we shouldn't stop posing such questions. They are deep problems and may hide some of the most important physics.

But, I'm afraid, there's a sting in the tail. Despite living in a world surrounded by these things (we are bound to a planet by a gravitational field, viewing our environment through oscillations in the electromagnetic field), we have no intuitive understanding of them (our normal life has not required us to develop one). Thus the only way we can study them is by looking at their mathematical properties. The only way to develop an intuitive feel for the meaning and workings of the electric field is to use it in calculations lots until you start to have a feeling for its properties and begin no longer to rely on having to always do the calculations in full to see the general way something is going to turn out. Analogies written by people who have already done this themselves can definitely help, but they are not a substitute for doing the calculations yourself because until you have done that you have no experience to relate the analogies to.

This is, I'm afraid, why physicists also get a bad reputation. We either say that it is impossible to explain to a layman, which makes us seem arrogant; or we give a mathematical explanation (which makes us seem elitist); or we try and give some kind of real world analogy only to have the recipient of the explanation say "But doesn't that mean this?" to which the answer is usually "No, it doesn't work like that" since they have no experience to pin the analogy to (thus making us seem obtuse). The short answer is: you can't understand physics until you have done at least some of the relevant physics --- sooner or later you have to get your hands dirty with the mathematics, because it's being used to describe something you have no experience of.

Sorry for the lengthy reply, I seem to have difficulty with making short posts!

14. Jul 31, 2009

### cepheid

Staff Emeritus
Re: What is an electric field???

Perhaps so, but I thought it was an awesome post though! Worth the read.

15. Jul 31, 2009

### sganesh88

Re: What is an electric field???

Excellent post jmb! You have hit the nail; Explaining the weakness in the foundation of Physics as well as the efforts one has to take, to understand what the present Laws of physics tell about nature..

But why nature follows such rigid mathematical relations is still a mystery (always taking care that acceleration always equals F divided by m and so on). Its sort of unsettling for me to see nature holding onto something rigidly.

16. Aug 1, 2009

### rockyshephear

Re: What is an electric field???

Brilliant! Thank you for taking the time to present that well-thought out answer to my question. It was enlightening, for sure. But as to the nature of truth, I think Descarte said it best. "I think, therefore I am." This we can know for sure. Whether you guys are really out there or not cannot be known. :)