Does potential depend on relative permittivity in a dielectric?

[Lindsayyyy]

Hi everyone,

I have a question about electric potentials and dielelectrics:

1. when I have a dielectri in the half space x<0 and air in x>0 is the potential steady at x=0?

2. does a potential depend on the relative permittivity ?


I know that the electric field gets weaker in a dielectric with 1/epsilon_r but what about the potential? I'm not sure here.

Thanks for your help in advance.

 

[szynkasz]

1. What electric field is applied?
2. Yes, it does in the same way as electric field.

 

[Lindsayyyy]

lets just talk about a general potential like

$$\Phi (\vec r) = \frac {1}{4\pi \epsilon_0} \frac {q}{|\vec r -\vec r_0|}$$ for x >0 and for x<0 the same one (+ epsilon_r for the permittivity).

are these potentials steady at x=0 ?

 

[szynkasz]

This is a potential from a point charge. It's value changes along X axis.

 

[ehild]

The electrostatic potential is continuous at the interface of two media. In your problem, it is the same at x=0 at both sides of the boundary.

ehild

 

[Lindsayyyy]

thank you very much.