# Electric fields in practice

1. Oct 27, 2006

### pivoxa15

Purcell said "One must be alert for every opportunity to bring the students into the world where an electric field is not a symbol merely, but something that crackles."

Why does an electric field crackle? Is it because electric fields are lines which connect charges, enabling them to exert forces on each other. When they do exert forces on each other, they move and when that happens, they collide with air particles and other charges around them in inelastic collisions hence release energy such as sound. They will also likely to give off electromagnetic waves since in the collisions they are likely to change directions and accelerate. The sound and light give us the impression of something that crackles i.e. electric spark. But all this can only happen given the existence of electric field lines. Hence electric fields manifest the spark which crackles. In other words, the crackles can only occur in electric fields so electric fields is something that crackles.
Correct?

This explanation is based on the assumption that electric field exist like the existence of an electron. However, does electric field exist like how electrons exist? I heard it was defined to allow charges to communicate without 'spooky action at a distance'.

This also brings about the question of electromagnetic waves. They are regarded exactly as light, which evidently does exist. So electromagnetic waves exist. Does the existence of light or electromagnetic waves suggest the existence of electric fields, given that electromagnetic waves are periodic propagations in the electromagnetic field.

There is also the issue of electric field themselves. Are electric fields always attached to charges that extend to infinity (which would mean the field is forever extending it)? But what about when charges come into existence through pair production? Does the field lines propagate at speed c through space to infinite extent at the instand the charge is created? What happens when the electric field reach another charge? Does it exert some momentum on it? I suppose it would if a wave was progating on the tip of the travelling field (which would mean the electron was accelerating non uniformly at the moment of its creation) but not otherwise?

Last edited: Oct 28, 2006
2. Oct 28, 2006

### leright

The electric field, or any "field" for that matter, is simply a mathematical construct that allows us to model experimental obervations. The electric field, in particular, describes the forces that charges feel when they are in the presense of other charges. I am only an undergraduate physics student, but I am pretty certain that there are no strongly accepted theories that explain what an electric field is, beyond the typical F = qE definition.

I've never bought the idea that the introduction of E-fields eliminate the action at a distance problem. The action at a distance problem is still there even with the idea of E-fields introduced. The fields MODEL the action at a distance.....they DO NOT explain action at a distance.

Last edited: Oct 28, 2006
3. Oct 28, 2006

### pmb_phy

It is quite more than that. And that was what Purcell was saying in that paragraph.
A force need not be exerted on anything for the field to have meaning. E.g. an electromagnetic wave has an existance beyond the force it exerts on particles. It can actually carry energy across space. In that sense the electric field is real and more than simply a construct mathematical.

Best wishes

Pete

4. Oct 28, 2006

### pivoxa15

According here http://en.wikipedia.org/wiki/Electric_field the electric field and other fields travel at c and only after E fields have reached particles can they exchange information so it definitely eliminates action at a distance.

But when it 'hits' or reaches another particle, can it exert momentum? Or can it exert momentum only if a wave is propagating along with it?
Also if it real, how would you detect it?

5. Oct 28, 2006

### leright

I did not know E-fields traveled at c.....can someone explain this? I knew electromagnetic waves propagated at c (where the direction of propagation is PERPENDICULAR to the E-field) but did not know E-fields propagate at c. Is this an experimental fact, or can it be deduced from other facts?

So, if it takes finite time for action at a distance to occur, this implies that some sort of particle is being exchanged, right? I'm sure there is some sort of explanation of this in particle physics, but I know nothing about particle physics.

6. Oct 28, 2006

### Staff: Mentor

Changes in E and B fields propagate at c, in a vacuum. Electromagnetic waves are an example of this, but not the only example.

In the quantum electrodynamical picture of electromagnetism, electric and magnetic forces are mediated on a microscopic scale (very microscopic! ) by the exchange of virtual photons. The classical picture using E and B fields arises on the macroscopic scale as the collective effect of bazillions and bazillions of virtual photons.

7. Oct 28, 2006

### leright

Is there any evidence for this idea?

What is a 'virtual' photon?

8. Oct 28, 2006

### quasar987

To expand on leright's question...

We can combine a couple of Maxwell's equations to obtain a wave equation:

$$\nabla^2\vec{E}+\frac{1}{c^2}\frac{\partial^2\vec{E}}{\partial t^2}=0$$

So progressive waves of velocity c are a solution to Maxwell's equations (provided we require that the wave solution also satifies the four maxwell's equations independantly; this is where the condition $\vec{E}\perp \vec{k}$ for a wave with no boundary conditions is from)

But does that imply that an E fields not propagating in the void in the form of a progressive wave of velocity c contradict Maxwell's equations? I don't imediately see the contradiction.

9. Oct 29, 2006

### StatMechGuy

Of course there's evidence for this idea. It won three theorists the Nobel Prize, and they don't give that out to theorists unless what they're saying is firmly experimentally tested. Now, we cannot see virtual photons directly, in the strictest since, but we have a theory that is ungodly accurate that involves their use, so we just roll with it. Nobody's ever "seen" an electron, strictly speaking, but we know they have to be there because as of right now it's the only logical conclusion.

10. Oct 30, 2006

### pivoxa15

Which three theorists? Which year?

I think it is impossible to see an electron like seeing a chair because of HUP.

11. Oct 30, 2006

### pivoxa15

I might have made a mistake when I said that electric fields travel at c. The information of force certainly do travel at c but the fields themselves?

In Classical Electromagetism by R.Good (the opening Purcell quote was taken from this same book), it said "Fields don't move: instead they have space and time derivatives." Is this true for non classical physics as well? i.e. fields in non classical physics don't move either?

What does a space derivative of a field mean? What would a space derivative of a stationary field be? Constant? That seems too trivial.

He also said that if we include relativity than in some frames, entire fields could disspear. I guess the field model is just something imaginary or non physical, there to prevent action at a distance. So fields are embedded in the frames of observation and is omnipresent there?

Last edited: Oct 30, 2006
12. Oct 30, 2006

### quasar987

Last edited: Oct 30, 2006
13. Oct 30, 2006

### lightarrow

A field, by definition, is a function (scalar, vectorial, tensorial ecc.) of the point in space and, in general, of time as well. So the value of a field changes, in general, from one point to another; the space derivative measures this change, for a fixed instant of time. The time derivative measures its changing in time for a fixed point of space, so the time derivative of a stationary field is zero.
Remember however that "stationary" means that the field don't explicitly depends on time; in this case it's the partial time derivative to be zero. This because there could be fields for which the point itself is a function of time. Example: the field of velocities v inside a moving fluid.

Last edited: Oct 30, 2006
14. Oct 30, 2006

### masudr

By the way that's supposed to be

$$\nabla^2\vec{E}-\frac{1}{c^2}\frac{\partial^2\vec{E}}{\partial t^2}=0$$

15. Oct 30, 2006

### masudr

Say we have a vector field, $\vec{E}\left(t, \vec{x}\right).$ It's time derivative and space derivatives are, respectively,

$$\frac{\partial\vec{E}}{\partial t}, \,\,\mbox{and}\,\, \frac{\partial\vec{E}}{\partial x}, \frac{\partial\vec{E}}{\partial y}, \frac{\partial\vec{E}}{\partial z}.$$

Last edited: Oct 30, 2006
16. Oct 31, 2006

### pivoxa15

So think of fields as vectors implanted in a reference frame which may change as time changes (partial time derivatives), or change as you move around the field (partial space derivative) but it does not move inside this reference frame (i.e the vectors don't migrate around). However, what happens if the charge associated with the field move? Would each vector just change to accomodate the charge but are always fixed in that place. I guess the information of the change would propagate at c but what is the physical form of it? It doesn't have to be EM waves if the particle hasn't accelerated.

In the same textbook, R.Good wrote "The most important single characteristic of a field is the energy it contains."

Last edited: Oct 31, 2006
17. Oct 31, 2006

### lightarrow

I'm not sure to have understood well your question; however I give you an analogy, then you can say if it has anything to do or not with your question:
you have a series of lamps along a line. If the first one is switched on and off, then the next one is switched on and off...and so on, you have the image of a light ball moving along the line.
The same is with fields. In a precise point of space, the electric (for example) field varies with time; in the next point, the same happen, with (in general) a different timing, so what you see is an EM wave, or any other kind of "perturbation", propagating in space. If this happens because of an accelerating charge or a charge moving with constant speed or anything else, doesn't change the principle.

18. Nov 1, 2006

### pivoxa15

I see what you are getting at but what other propagations are there apart from EM waves?

19. Nov 4, 2006

### lightarrow

There are many others fields, especially in a matter medium. In the void: gravitational perturbations, for example.

20. Nov 4, 2006

### quasar987

The big ripple on top of the merchandise truck in Matrix 2 when they fight on the highway.