# Electric Displacement field? what is it?

1. Jun 19, 2008

### iLIKEstuff

So i have been delving into the realm of electrodynamics for the first time in an independent study that i'm doing but i am having trouble conceptualizing some vital concepts. one of them is D, the electric displacement field.

Most texts don't even bother to explain what D is or where it comes from. they mostly introduce it as a continuity condition. i'm confused since i'm not sure if it is an actual real thing or not (like an E field). perhaps i'm taking the wrong approach in trying to understand it.

So we have two plates that are oppositely charged and we place a polarizable material in between these two plates. the E field is less inside the material because of the attraction of opposite charges to the plates (which sets up an opposite E field inside). now where is D? the text i'm reading now (electrons in solids by richard bube) says that D is the same in between the material and the plates and inside the material. what does that mean? the charge density is the same everywhere in between the plates?

now D has units of C/m^2 or charge per area meaning that it is a charge density or charge flux. since it is called a field, which means "action at a distance" i'm not seeing the action that is taking place at a distance? i'm trying to relate this to the E field. which can be easily understood by setting up the oppositely charged plates like we did before (the field exists in between the plates). so where is D? how can you set up D?

my main question is what is D? where does it come from? what contributes to it?

i talked to one of the phd students in the lab and he said that it is entirely a material property and its description gets really hairy when you get to nonisotropic materials or large E fields like lightning and he started blabbering (that's what it sounded like to me) about some crazy math i didn't understand. so for you brainiacs outt here...please no talk about tensors.

Thanks guys.

edit: also i'm trying to think about the analogy between the e-field and the h-field. i remember when i took the basic EM physics class and learned about lorentz force they were always talking about an applied B field (to deflect the charge in motion). is this the same B-field when talking about maxwell's equations? if it is, then there is an H field set up by a dipole and the flux lines are the B so then by analogy you set up an E field with oppositely charged plates (a dipole?) and the flux lines are D?

Last edited: Jun 19, 2008
2. Jun 19, 2008

### lbrits

It's not as fundamental as E. Essentially, dielectric materials pick up their own induced dipole moment when placed in an electric field (they become polarized), which, in turn, distorts the electric field. If you try to keep track of E as it back-reacts, you're likely to get confused. So we introduce $$D = \epsilon_0 E + P$$. It turns out that Maxwell's equations are "nice" when expressed in terms of D.

In short, "E" is the thing that drives electrons and pith balls, obeys Gauss' law, is divergenceless, and all that. We use "D" to simplify the math in linear materials.

I highly recommend Griffith's electrodynamics book. It's the de facto standard for learning E&M.

The relation between H and B is the same, if only for an unfortunate minus sign =)

3. Jun 20, 2008

### cabraham

I'm not following. "D" obeys Gauss' law just like "E". As far as being "divergenceless" goes, both have non-zero divergence when charges are present.

Regarding H and B, can anyone draw an analogy between E/D vs. H/B? What is the relation between B and H, and how is it like that of D/E?

I'm not aware of which is more fundamental, so I'm just curious as to how you arrive at your conclusions. Thanks in advance.

Claude

4. Jun 20, 2008

### lbrits

Sorry, I wasn't in a clear state of mind when I wrote this. By Gauss' law I meant in terms of real charges. The distinction between free and bound charges is a bit artificial, as both are forms of charge. I think the point is that you can't necessarily write D in terms of a scalar potential, because the permittivity varies with position.

5. Jun 23, 2008

### PhilDSP

Maybe it's worthwhile to look at some of Maxwell's writings or those of his contemporaries. Maxwell believed that there was in fact some type of medium even in the vacuum which transported the wave energy (i.e. displacement current). He called that medium ether or aether.

The "action at a distance" is the event of, for instance, an antenna picking up the wave energy that was transmitted from a remote site.

More recent views have tended to wave away the need for something similar, such as what Ibrits posits. The problem with that is of course that some type of miracle must occur to transport the energy through a vacuum. If you are comfortable with the idea of action at a distance and believe it is rational then you need not look or think further.

The strange thing is that you need to move the charges up and down, for instance, if you want the wave to proceed sideways. The implication is that the charges themselves do not provide the propulsion to launch the wave.

Last edited: Jun 23, 2008
6. Jun 24, 2008

### pzlded

From the URL
http://farside.ph.utexas.edu/teaching/316/lectures/node116.html

The equation relating magnetism to current is:
$$\oint B\cdot\partial r=\mu_{0}(I+I_{D})$$

D in this equation violates Ampere’s law. There is generally a problem with relating point charges to voltage. Resistors with current normally contain a linear voltage gradient. No infinitely sized sheet of point charges exists within a resistor to create a linear voltage gradient. The only point charge configuration that produces a linear voltage gradient is an infinitely sized sheet of point charges. A dipole does not contain a linear voltage gradient, neither does a collection of aligned dipoles.

A website that includes an alternative to sheet point charge based linear voltage gradients is:
http://mysite.verizon.net/richarddesaneis/