Finding D2 for a Dielectric Interface with Given Conditions

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SUMMARY

The discussion focuses on solving for the electric flux density D2 across a dielectric interface defined by the equation 4y + 3z = 12. The initial electric flux density is given as D = ax + 3ay + 2az (micro) C/m², with the dielectric constant on the second side being εr2 = 2. The solution involves calculating the electric field E1 from D using the relationship D = εE, followed by determining the normal and tangential components of the electric field across the interface to find D2.

PREREQUISITES
  • Understanding of dielectric materials and boundary conditions in electromagnetism.
  • Familiarity with electric flux density and electric field relationships, specifically D = εE.
  • Knowledge of vector calculus, particularly unit vectors and components of vectors.
  • Basic principles of electrostatics, including the concept of relative permittivity (εr).
NEXT STEPS
  • Study the derivation of electric field components across dielectric interfaces.
  • Learn about the application of Gauss's Law in dielectric materials.
  • Explore the concept of electric displacement field (D) in different media.
  • Investigate boundary conditions for electric fields at dielectric interfaces.
USEFUL FOR

Students and professionals in electrical engineering, particularly those focusing on electromagnetism and dielectric materials, will benefit from this discussion.

kloong
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Urgent: Boundary Condition querries.

Homework Statement


Question given: A dielectric interface is described by 4y+3z=12. The side including the origin is free space and its electric flux density, D=ax+3ay+2az (micro) C/m2. On the other side, (Epsilon)r2 = 2. Find D2.


Homework Equations





The Attempt at a Solution


Ok, so this is how i try to solve it:
1. I get the unit vector of the equation given(but only make use of 4y + 3z).

2. Then i get the E1. (by using the eq D=(eps)E) thus getting: (ax+3ay+2az)(micro)eps^-1.
>> is it correct? because i am familiar doing it with E and not D. am i suppose to do it this way? or are there any better alternate ways?

3. Then i went on to get E1n by using the equation (E . an)(an).

4. Then E1t. (E1 = E1n + E1t)

5. Then E2n ( (Eps)r1 E1n = (Eps)r2 E2n) )

6. And finally, E2 = E2n + E2t. And using the eq D=(eps)E to get D2.


thank you.
 
Last edited:
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One thing I see missing from all this is what the QUESTION itself is! What exactly are you trying to find?
 
the second step. if it is correct if i change the given D to E1 using the equation D=(eps)E.

apart from that, i want to know if my way of doing it is correct or not.
 

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