Solving Boundary Conditions for Electric Field in Dielectric Media

In summary, the conversation is about solving a problem involving finding the electric field in two lossless dielectric regions with different permittivity values. The question is asking for the electric field in the second region and the boundary conditions at the interface between the two regions. One member suggests using the tangential components of the electric field to solve the problem, while another explains that only the normal component changes when crossing the interface. The conversation ends with the acknowledgment that the problem has been solved.
  • #1
Electro
48
0
Greetings everyone:
I'm trying to solve a problem which requires finding the electric field. I've been pondering on this problem for a while but still no results. The book doesn't give any hints or clues on how to tackle this kind of problems so I would really appreciate some of your suggestions.

Assume that the z= 0 plane separates two lossless diaelectric regions with Epsilon(r1) = 2 and Epsilon(r2)=3. If we know that E1 in region 1 is 2y i - 3x j + (5+z) k, what is E2?
 
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  • #2
What are the boundary conditions on the electric field at the interface between the two dielectric regions?
 
  • #3
Thanks Siddharth, but if we draw a picture of the two media, geometrically we can conclude that E1t = E2t where E1t=E1-E1n and the same with E2t (I guess you get the picture). I don't see how this would help. Moreover we are dealing with 3-D ( I guess I might have understood it if it was 2-D).
Thanks

I'm editing the post: Thanks for your help, I understand it now.
 
Last edited:
  • #4
Electro said:
Thanks Siddharth, but if we draw a picture of the two media, geometrically we can conclude that E1t = E2t where E1t=E1-E1n and the same with E2t (I guess you get the picture). I don't see how this would help. Moreover we are dealing with 3-D ( I guess I might have understood it if it was 2-D).
Thanks

I'm actually dealing with a similar problem right now. The way I understand it, is that the two boundary conditions are:

[tex] E_{1t} = E_{2t} [/tex]
[tex] \vec a _{n2} \cdot (\vec D_1 - \vec D_2) = \rho_s [/tex]

For the first one,
[itex] E_{1t} = E_{2t} [/itex] means the tangential components are the same. This tripped me up a bit... and I'm still a little uneasy doing these problems. Anyhow you have a plane that separates the media [itex] z = 0 [/itex]. So what can you say about the relationship between all the vectors of [itex] \vec E_1(x,y,z=0) [/itex] and [itex] \vec E_2(x,y,z=0) [/itex].
All of those vectors are tangential to the interface. So you can conclude that only the normal component (in this case it would be [itex] E_{z2}, [/itex]) is going to change when crossing the interface. Since you know that the tangential components are the same (from the relation above), you are left with:

[tex] \vec E_2 = \vec a_x E_{1x} + \vec a_y E_{1y} + \vec a_z \bar E_{2z} [/tex]

where the bar was used for emphasis on[itex]\bar E_{2z} [/itex] (the z component of the vector).
 

1. What is the electric field?

The electric field is a physical quantity that describes the force exerted on a charged particle by other charged particles in its vicinity. It is represented by a vector and is measured in units of newtons per coulomb (N/C).

2. How do you calculate the electric field?

The electric field can be calculated by dividing the force acting on a charged particle by the magnitude of the charge of that particle. In equation form, it is represented as E = F/q, where E is the electric field, F is the force, and q is the charge.

3. What is the difference between electric field and electric potential?

The electric field and electric potential are both related to the concept of electric charge, but they represent different physical quantities. The electric field describes the strength and direction of the force acting on a charged particle, while electric potential describes the energy needed to move a charged particle from one point to another in an electric field.

4. How is the electric field affected by distance?

The electric field follows an inverse-square law, meaning that as distance from a charged particle increases, the electric field decreases proportionally. This relationship is represented by the equation E ∝ 1/r², where E is the electric field and r is the distance.

5. What are some real-world applications of electric fields?

Electric fields have many practical applications in our daily lives. Some examples include the functioning of electronic devices, such as computers and cell phones, as well as the operation of electric motors and generators. Electric fields are also used in medical equipment, such as MRI machines, and in industrial processes, such as electroplating and welding.

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