Dielectric-Dielectric Boundary Conditions Problem

In summary, the problem can be found at http://whites.sdsmt.edu/classes/ee382/homework/382Homework4.pdf and the goal is to find the electric displacement vector at the boundary between two materials. The boundary is located at y=0 and the problem involves using the material constants epsilon1 and epsilon2. The solution involves evaluating the given vector at y=0 and adding the transverse and normal components of the electric displacement vector. The final expression should be double checked for accuracy.
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Homework Statement


The problem can be found http://whites.sdsmt.edu/classes/ee382/homework/382Homework4.pdf" [Broken]. It is the first one. Note: The subscript x = 0 is supposed to be y = 0 (the teacher typed it in wrong).


Homework Equations


[tex]\vec{\boldsymbol{D}}_{2t} = \epsilon_{2}\vec{\boldsymbol{D}}_{1t}/\epsilon_{1}[/tex]

[tex]\vec{\boldsymbol{D}}_{2n} = \vec{\boldsymbol{D}}_{1n}[/tex] (assuming [tex]\rho_{s} = 0[/tex] because it isn't mentioned)

[tex]\vec{\boldsymbol{D}}_{2} = \vec{\boldsymbol{D}}_{2t} + \vec{\boldsymbol{D}}_{2n}[/tex]


The Attempt at a Solution


[tex]\vec{\boldsymbol{D}}_{2t} = \epsilon_{2}\vec{\boldsymbol{D}}_{1t}/\epsilon_{1} = \epsilon_{2}(\hat{\boldsymbol{a}}_{x}\alpha + \hat{\boldsymbol{a}}_{z}\gamma)/\epsilon_{1}[/tex]

[tex]\vec{\boldsymbol{D}}_{2n} = \vec{\boldsymbol{D}}_{1n} = \hat{\boldsymbol{a}}_{y}\beta[/tex]

[tex]\vec{\boldsymbol{D}}_{2} = \vec{\boldsymbol{D}}_{2t} + \vec{\boldsymbol{D}}_{2n} = \epsilon_{2}(\hat{\boldsymbol{a}}_{x}\alpha + \hat{\boldsymbol{a}}_{z}\gamma)/\epsilon_{1} + \hat{\boldsymbol{a}}_{y}\beta[/tex]

Is this all there is to it, or do I need to do something with the y = 0 stuff? My teacher told me that I'm supposed to evaluate the given vector at y = 0, but since the vector contains no y's, it doesn't make any sense to me. It seems kind of redudant to me, actually. Do you suppose the y = 0 is just telling me where the boundary is located (if I wasn't able to figure it out from the figure)? If someone could cure me of my confusion, that would be great. Thanks.
 
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  • #2


Hello,

Thank you for your post. It seems like you have the right idea for solving this problem. The y=0 notation is simply indicating the location of the boundary between the two materials. In this case, the boundary is located at y=0 and the problem is asking for the electric displacement vector at this boundary.

Your solution looks correct, but I would suggest double checking your final vector expression to make sure it is in the correct format. Also, make sure to include the values for the material constants epsilon1 and epsilon2. Let me know if you have any further questions or need help with anything else. Good luck!
 

What is a dielectric-dielectric boundary condition problem?

A dielectric-dielectric boundary condition problem is a phenomenon that occurs when two dielectric materials are in contact with each other and there is an electric field present at the interface between them. This creates a boundary condition where the electric field and other properties of the materials need to be taken into account in order to accurately model the behavior of the system.

How do dielectric-dielectric boundary conditions affect electric fields?

Dielectric-dielectric boundary conditions can have a significant impact on electric fields. When two dielectric materials are in contact, the electric field at the interface will be affected by the properties of both materials. This can lead to changes in the strength and direction of the electric field, as well as the distribution of charge in the materials.

What are the challenges of solving dielectric-dielectric boundary condition problems?

One of the main challenges of solving dielectric-dielectric boundary condition problems is accurately modeling the behavior of the materials at the interface. This requires taking into account the properties and behavior of both materials, as well as the interaction between them. Additionally, the complexity of the problem increases with the number of dielectric interfaces present in the system.

What are the applications of dielectric-dielectric boundary conditions?

The study of dielectric-dielectric boundary conditions has many important applications in various fields, including electrical engineering, materials science, and physics. It is especially relevant in the design and analysis of electronic devices, such as capacitors, circuit boards, and semiconductors. Understanding the behavior of electric fields at dielectric interfaces is crucial in optimizing the performance and efficiency of these devices.

How are dielectric-dielectric boundary conditions solved?

Different methods can be used to solve dielectric-dielectric boundary condition problems, depending on the complexity of the system and the desired level of accuracy. These methods include analytical solutions, numerical techniques such as finite element analysis, and experimental approaches. The choice of method depends on the specific problem and the resources available for solving it.

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