Induced charge density by non-uniform dipole density in dielectric?

In summary, Feynman is saying that if the charges are evenly distributed throughout a dielectric, then there is no net charge, but if there is an increase in charge at one area, then a net charge will be present.
  • #1
quasar987
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In chapter 10 section 3 volume 2 of the Feynman lectures on physics, there is a passage that I can't force myself to agree with. He says, talking about the polarization vector of dielectrics,

First consider a sheet of material in which there is a certain dipole moment per unit volume. Will there be on the average any charge density produced by this? Not if P is uniform. If the positive and negative charges being displaced relative to each other have the same average density, the fact that they are displaced does not produce any net charge inside the volume. On the other hand, if P were larger at one place and smaller at another, that would mean that more charge would be moved into some region than away from it; we would then expect to get a volume density of charge.

Can someone explain this perhaps differently?

I really don't see how a non-uniform polarisation vector across a dielectric have to do with charge density. If P is larger at one place, it is either because 1) E is greater there, or 2) the density of atoms N is greater there. But in either case, the total charge in a volume element remains that of the sum of the atoms, which is null for regular dielectric atoms regardeless of the number of them N in that volume or of the magnitude of the "dipole distance" [itex]\vec{d}[/itex] (as in [itex]\vec{p}=q\vec{d})[/itex].
 
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  • #2
Feynman can entertain, but avoids the nitty gritty.
Try this picture: One long molecule having +q at one end and -q at the other, so its dipole moment is qL. Then next to it, a molecule with +- 2 q at the ends. Sort of like this: -q-----+q -2q-----+2q.
This represents a P that is increasing to the right. If you look in the middle, there is a net charge of -q. This corresponds to
\rho_bound=-div P (in Gaussian units).
 
  • #3


I understand your confusion and I would like to clarify this concept for you. The key to understanding induced charge density in a non-uniform dipole density in dielectric lies in the fact that polarization (P) is a vector quantity with magnitude and direction. In the context of dielectrics, polarization refers to the alignment of dipole moments within the material.

Now, let's consider a sheet of material with a non-uniform dipole density, meaning that the dipole moments are not evenly distributed throughout the material. This means that the polarization vector will also not be uniform throughout the material. In regions where the dipole moment is larger, the polarization vector will also be larger, and in regions where the dipole moment is smaller, the polarization vector will be smaller.

According to Coulomb's law, the electric field (E) is directly proportional to the charge density (ρ), where E = ρ/ε_0, with ε_0 being the permittivity of free space. Therefore, in regions where the polarization vector is larger, the electric field will also be larger, resulting in a higher charge density. This is because the dipole moments are creating an electric field, and the non-uniform distribution of these dipole moments results in a non-uniform electric field, which in turn leads to a non-uniform charge density.

In simpler terms, the non-uniform dipole density creates a non-uniform electric field, which then leads to a non-uniform charge density. I hope this explanation helps to clarify the concept for you.
 

1. What is induced charge density?

Induced charge density refers to the electric charge that is created on the surface of a dielectric material when it is placed in an external electric field. This charge is caused by the realignment of the dipoles within the material.

2. How is induced charge density related to non-uniform dipole density?

Induced charge density is directly proportional to the non-uniform dipole density within a dielectric material. This means that the greater the difference in dipole density within the material, the higher the induced charge density will be on its surface.

3. What causes non-uniform dipole density in a dielectric?

Non-uniform dipole density in a dielectric material can be caused by various factors, such as the presence of impurities, defects, or uneven distribution of molecules within the material. It can also be influenced by external factors, such as temperature and electric field strength.

4. How does induced charge density affect the behavior of a dielectric material?

The induced charge density on the surface of a dielectric material creates an electric field that opposes the external electric field. This results in a decrease in the overall electric field within the material, making it less susceptible to the external field. This phenomenon is known as dielectric shielding.

5. What are the practical applications of induced charge density by non-uniform dipole density in dielectric materials?

Induced charge density by non-uniform dipole density is important in various technological applications, such as capacitors, insulators, and electronic devices. It also plays a crucial role in the functioning of living organisms, such as in the polarization of cell membranes.

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