What are the Boundary Conditions for Dielectric Interfaces?

In summary, the conversation discusses the relationship between the D field and free surface charge density in an infinite dielectric material with a boundary. It is suggested that the D field should be the same on both sides of the boundary, but it is not clear how to prove this for a dielectric material. It is clarified that the D field is the same for both air and the dielectric, but the E field will differ due to the difference in epsilon values. It is then explained that this is due to the definition of D and Gauss's Law for materials, which only considers the free charge and not the material itself.
  • #1
plmokn2
35
0

Homework Statement


Say I have a boundary between two dielectrics then it's easy to show using a gaussian pillarbox that:
D(1)-D(2)=free surface charge density=s
where D(1) is the component of the first medium normal to the surface.
But suppose that there's nothing else apart from two infinite dielectrics with a constant free charge density between then, how would I work out what the actual values of D(1) and D(2) are rather than just the difference?

The Attempt at a Solution


It seems reasonable that the D field should be the same on both sides so that D=s/2 but I'm not sure how I'd prove this?

Any help appreciated.
 
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  • #2
I'm having a hard time interpreting what you are asking. Could you draw it?
 
  • #3
I think my question was badly worded/ I've probably misused some terminology.

I suppose my actual qustion is:
Its obvious from the symmetry that for an uncharged nonconducting non-dielectric that if you put a surface charge density s on it the field above is the same magnitude as the field below: D=s/2.

But suppose that the material is a dielectric then I'm not sure how you prove what the D field is above the surface (in air) and below the surface (in the dielectric) (under the same condition of the dielectric being infinite with surface charge s and no other free charge anywhere)

Hope this is a bit clearer, please say if it isn't.
 
  • #4
Oh, well D is going to be the same for both air and the dielectric, but E will be different because E is D/(epsilon) which will change between the two (epsilon_0 for air and dielectric epsilon in the dielectric). Is this what you are asking about?
 
  • #5
That's it.

Its probably really obvious but how do you know that D has to be the same on both sides of the boundary?
Thanks
 
  • #6
It comes from the way D is defined. After its whole redefinition then you just get a Gauss's Law for materials which goes as

[tex]\iint \mathbf{D} \cdot d\mathbf{a} = \sigma_f[/tex]

and that means that the only thing that you care about is the free charge, which will be the same on both sides.
 
  • #7
Thanks.
 

What is the boundary between dielectrics?

The boundary between dielectrics is the interface between two materials with different electrical properties, such as two insulating materials or an insulating material and a conducting material.

How does the boundary between dielectrics affect electric fields?

The boundary between dielectrics can affect electric fields in several ways. It can cause the electric field to bend or change direction, it can cause the electric field to become stronger or weaker, and it can also cause the electric field to reflect or refract.

What is the importance of understanding the boundary between dielectrics?

Understanding the boundary between dielectrics is crucial in many areas of science and engineering. It is essential for designing and analyzing electronic devices, such as capacitors, insulators, and semiconductors. It is also important for understanding the behavior of electromagnetic waves and their interactions with materials.

What factors affect the behavior of the boundary between dielectrics?

The behavior of the boundary between dielectrics is influenced by several factors, including the electrical properties of the materials, the angle of incidence of the electric field, and the frequency of the electric field.

How can the boundary between dielectrics be manipulated?

The boundary between dielectrics can be manipulated by changing the physical characteristics of the materials, such as their thickness or composition. It can also be controlled by applying an external electric field or by using specialized coatings or layers to alter its behavior.

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