Dielectric interface plate capacitor at angle alpha

[lena_2509]

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.

Relevant Equations

E_1*sin a_1= E_2* sin a_2

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 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?