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I am studying Introduction to Electrodynamics by Griffiths and I came along a concept I cannot seem to understand properly. The concept of free charge AND bound charge. I do not understand how we can have both. I understand bound is created by the presence of an E field and a dielectric. So where does the free charge come from if we are inside a dielectric ? Here is a quote from the book talking about it

In Sect. 4.2 we found that the effect of polarization is to produce accumulations of bound charge, $\rho_b= - \vec{\nabla} \cdot \vec{P}$ within the dielectric and $\sigma_b=\vec{P}\cdot\hat{n}$ on the surface. The field due to polarization of the medium is just the field of this bound charge. We are now ready to put it all together: the field attributable to bound charge plus the field due to everything else (which, for want of a better term, we call free charge). The free charge might consist of electrons on a conductor or ions embedded in the dielectric material or whatever; any charge, in other words, that is not a result of polarization.

Timaeus
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user1198778
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6 Answers6

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Imagine a blob of liquid water. Each molecule is polar because the electrons are closer to the oxygen than the hydrogens. Without a large external electric field, the water is moving around bumping this way and that way with basically random orientations.

Now while in orbit make a very large parallel plate capacitor,charge it up and put your blob of water in between the plates. They still move around and bump into each other, but now if the hydrogen side is pointing in the direction of the electric field, it becomes harder (energy wise) to change that orientation. Over time the water can start to develop a preferred net polarization. How strong can depend on the temperature as well as the strength of the field. This is your polarization. Im your mind imagine looking at a line through the water and if the field was much stronger than the temperature induced vibrations you might see the individual charged parts of each water molecule line up like

  • +- +- +- +- +- +-

where each +- is the two charged sides of a water molecule, so they are always always next to each other. And to someone that only cared about net charge they might look and see that it looks like

  • +.....................-

So it might look like there is only some surface charge. But that plus on the one end is bound to the negative part right by it and that negative one (on the other side of the surface) is bound to the positive part right next to it.

Now no water is pure, so you can imagine putting salt in the water and some of the NaCl crystals really do break up into Na and Cl ions (even the water itself has ions, some of the H20 molecules break up into H and OH ions) and those ions really have a net charge each and they can move around. Those are the free charges, in an external field they can move around (as charge carrier for a current, or going to the surface) and these positive and negative charges really can be far away from each other.

The bound charges aren't just affected by the parallel plate capacitor, they are affected by each other and by the free charge, but if you didn't care about the bound charges because you only care about the ions and electrons that can be added or removed from the water, then you can work with the displacement field $\vec{D}$ that ignores the bound charge. Then you get something that tracks what you care about.

An example is a high-dielectric capacitor. If all you care about is how it works as a capacitor, and you don't care about where each polarized molecule is located, then you can compute the $\vec{D}$ field inside just like for a normal capacitor.

Timaeus
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A dielectric is not a conductor, thus there are no electrons that are able to flow through it. However atoms or molecules within may be able to be polarised making an electric dipole, which can align to enhance or anti-align to reduce the applied field. This is bound charge.

In a metal or in free space the electrons flow and are, in a sense, free. They are able to move around independent of any fixed atom.

I suppose there will also be (but not in any course I ever did) materials in which there exist charges that are able to move (free) and those that are stuck together as atoms to be polarised (bound). Your book may include into the free definition anything that is not a neutral atom being polarised.

Editing in response to an update of the question look at the Wikipedia page for curl: http://en.wikipedia.org/wiki/Curl_%28mathematics%29. If in any of the pictures you imagine that at each point where there is an arrow, there is an atom with electric dipole moment in the magnitude and direction of the arrow. From this you can see how there may be a curl in the polarisation.

Eddy
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I would write this as a comment to Eddy's answer which is very precise, but no enough point to do so. Anyway,

a composite material made of thin layers of dieletric separated by thin layers of conductor might fit your case. Or particles of conductor eveloped by some dielectric layer might as well.

Giorgio Pastasciutta
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In conductors such as metals there are free electrons available. These free electrons are random in motion such that net electric field inside a conductor is zero. Current passes unless we apply an external electric field to metallic conductors. These free electrons inside the conductor are free charge, whereas in the case of dielectrics there are no free electrons, because the electrons are bound by molecular forces. By the application of an electric field electrons gets displaced forming dipoles. An external electric field that is applied to a dielectric material causes a displacement of bound charged elements. These are elements which are bound to molecules and are not free to move around the material. Applying Gauss' Law let us enclose a surface $S$ enclosing bound charge

$$Q_{\text{bound}} =- \oint_S P.dS \, ,$$

where $P$ is the polarization vector of dielectric material.

QuantumBrick
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srinivas
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The electric Shaver of a conductor and insulator can be understood on the basis of free and bound charges in metallic conductor the electron in outermost shell of the atom are loosely bound to the nucleus and hence can easily get detect and move freely inside the material when an external electric field is applied then the direction opposite to the direction of applied electric field this charge are called Freecharge

Abhishek
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Maxwell's equations are limited because they utilize Gauss's law of electrostatics. Therefore, the electric field is always proportional to static charge density, whether free or bound. If one were to conceptualize a third form of charge density (mobile charge density), then Ohm's law would become implicitly incorporated into a more generalized form of Maxwell's equations. This would limit some of the conceptual issues in the conventional theory. A good paper proving these issues with conventional theory can be found here: https://chemrxiv.org/articles/Maxwell_s_Equations_versus_Newton_s_Third_Law/6297185

Dr. Electrochem
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