• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Dielectric interface plate capacitor at angle alpha

5
0
Homework Statement
Consider a plate capacitor with a dielectric interface (\epsilon = \epsilon_0*\epsilon_r, thickness=d) tilted at the angle \alpha . Outside the interface \epsilon = \epsilon_0. Without dielectric interface is the field \vec{E}=E_0*\vec{e_z}. Determine the E-field inside and outside the dielectric interface at the angle \alpha.
Homework Equations
E_1*sin a_1= E_2* sin a_2
TheoAufgabe.png

Consider a plate capacitor with a dielectric interface (\epsilon = \epsilon_0*\epsilon_r, thickness=d) tilted at the angle \alpha . Outside the interface \epsilon = \epsilon_0. Without dielectric interface is the field \vec{E}=E_0*\vec{e_z}.
Determine the E-field inside and outside the dielectric interface at the angle \alpha (a).
My first attempt was to determine the E-field for the parallel and the perpendicular component at the angle \alpha=0 inside and outside the medium.
Inside the medium:
for the parallel component→ E_1*sin a_1= E_2* sin a_2 with a_1 = 0 → E_2=a_2=0
So inside the dielectric interface the parallel component is zero
for the perpendicular component: epsilon_1*E_1*cos a_1 = epsilon_2*E_2*cos a_2 with a_1= 0 → E_2=epsilon_1/epsilon_2* E_1
Outside the medium the electric displacement field D represents how an electric field E influences the organization of electric charges in a given medium. In electric field is D = epsilon_0*E +P.
But how do I determine the field for any other angle alpha ? Could I use the equations from the first attempt with a_1≠0 ?
 

rude man

Homework Helper
Insights Author
Gold Member
7,511
667
Homework Statement: Consider a plate capacitor with a dielectric interface (\epsilon = \epsilon_0*\epsilon_r, thickness=d) tilted at the angle \alpha . Outside the interface \epsilon = \epsilon_0. Without dielectric interface is the field \vec{E}=E_0*\vec{e_z}. Determine the E-field inside and outside the dielectric interface at the angle \alpha.
Homework Equations: E_1*sin a_1= E_2* sin a_2
View attachment 250691
What changes occur to an E vector normal to an interface between media of differing permittivities as it passes from one medium to another?

What changes occur to an E vector tangent to an interface between media of differing permittivities as it passes from one medium to another?

Can you resolve an oblique E vector into normal and tangent components, determine those changes, and from them determine the new E vector magnitude and direction inside the dielectric?

And can you check your work by line-integrating the new E vector along its new zig-zag path to verify that the potential difference between the plates is the same along this new path as it is along a path well beyond, and outside, the dielectric?
 

Want to reply to this thread?

"Dielectric interface plate capacitor at angle alpha" You must log in or register to reply here.

Related Threads for: Dielectric interface plate capacitor at angle alpha

Replies
6
Views
19K
Replies
10
Views
6K
Replies
3
Views
595
Replies
2
Views
6K
Replies
5
Views
881
Replies
6
Views
7K
Replies
8
Views
4K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top