Electric field in a second dielectric given a 2 dielectric system

In summary, the approach to finding the tangential and normal electric fields was correct, as shown by the equation ##E_{tan1}=E_{tan2}## and the use of ##D=\epsilon E##. The solution was found to be ##E_2=i+\frac 3 2 j+2k##, based on the values of ##E_1=2i+3j+4k V/m## and ##\epsilon_1=2\epsilon_0##. There was no surface charge at the boundary, so ##D_{N1}=D_{N2}##.
  • #1
willDavidson
50
6
Homework Statement
The boundary between dielectric regions is defined by the plane ##x+2y+3z=10##. The region containing the origin is refereed to as medium 1 ##(x+2y+3z=10)## and is assumed to have a permittivity ##\epsilon_1=2\epsilon_0##. Medium 2 is assumed to be the free space of vacuum. The fields in both regions are static and uniform. If ##E_1=2i+3j+4k## ##V/m##. Find E2. No surface charge is presented at the boundary.
Relevant Equations
##E_1 \epsilon_1=E_2 \epsilon_2##
##\oint_S E \cdot dl=0##
##\oint_S D \cdot ds##
I tried approaching this by finding the tangential and normal electric fields. Is this the correct approach? I've attached a drawing of the surface provided.

##\oint_S E \cdot dl=0##
##E_{tan1}\Delta x-E_{tan2}\Delta x=0##

We know that
##E_{tan1}=E_{tan2}

Next, we can find the normal component using
####\oint_S D \cdot ds##
##D_{N1}\cdot dS-D_{N2}\cdot dS=Q##
##D_{N1}-D_{N2}= \frac Q {dS}##
##D_{N1}-D_{N2}=\sigma##

Since the problem defined no surface charge at the boundary
##D_{N1}-D_{N2}=0##
##D_{N1}=D_{N2}##

Now we use
##D=\epsilon E##
##E_1 \epsilon_1=E_2 \epsilon_2##
##E_2=\frac {\epsilon_1} {\epsilon_2}E_1##

Solution
##\epsilon_1=2\epsilon_0##
##E_2=\frac 1 2 E_1##
##E_1=2i+3j+4k V/m##
##E_2=\frac 1 2 (2i+3j+4k) V/m##
##E_2=i+\frac 3 2 j+2k##
 

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  • #2
May I suggest computing En1 and Et1 at the boundary?
 
  • #3
I'm sorry. My mistake. I didn't realize the post was so old . The right panel presented it as without answer.
 

Related to Electric field in a second dielectric given a 2 dielectric system

What is an electric field?

An electric field is a physical quantity that describes the strength and direction of the force exerted on a charged particle by other charged particles or by an external electric field.

What is a dielectric?

A dielectric is a material that does not conduct electricity and can be polarized by an electric field, resulting in the displacement of charge within the material.

What is a two dielectric system?

A two dielectric system refers to a setup where there are two different dielectric materials present, with an electric field passing through both of them.

How is the electric field affected by the presence of a second dielectric?

The presence of a second dielectric in a system can change the electric field by altering the distribution of charge and the strength of the electric field within the system.

What factors influence the electric field in a second dielectric?

The electric field in a second dielectric is influenced by the dielectric constant, thickness, and orientation of the material, as well as the strength and direction of the external electric field.

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