Find electric field inside a material

[Istiak]

Homework Statement

An infinite slab of insulating material with
dielectric constant K and permittivity $\epsilon = K \epsilon_0$ is placed in a uniform electric field of magnitude $E_0$ . The field is perpendicular to the surface of the material. Find the magnitude of the electric field inside the material.]

Relevant Equations

$\vec D=\epsilon\vec E$

$\oint \vec D\cdot d\vec a=q_{f_{enc}}$

From the second equation I get that,
$\vec D =\frac{q}{4\pi \vec r^2}\hat r$
From first equation I get that

$\vec E = \frac{q}{4\pi \vec r^2 \epsilon}=\frac{q}{4\pi \vec r^2 K \epsilon_0}$
But I saw that the answer is $\vec E=\frac{\vec E_0}{K}$
While writing the comment my mind said, $\vec E_0=\frac{q}{4\pi \vec r^2 \epsilon_0}$

So easily, $\vec E= \frac{\vec E_0}{K}$

Or should I do the process some other way?

 

[dlgoff]

Homework Statement:: An infinite slab of insulating material with
dielectric constant K and permittivity $\epsilon = K \epsilon_0 is placed in a uniform electric field of magnitude$E_0## . The field is perpendicular to the surface of the material. Find the magnitude of the electric field inside the material.]
Relevant Equations:: $\vec D=\epsilon\vec E$

$\oint \vec D\cdot d\vec a=q_{f_{enc}}$

From the second equation I get that,
$\vec D =\frac{q}{4\pi \vec r^2}\hat r$
From first equation I get that

$\vec E = \frac{q}{4\pi \vec r^2 \epsilon}=\frac{q}{4\pi \vec r^2 K \epsilon_0}$
But I saw that the answer is $\vec E=\frac{\vec E_0}{K}$
While writing the comment my mind said, $\vec E_0=\frac{q}{4\pi \vec r^2 \epsilon_0}$

So easily, $\vec E= \frac{\vec E_0}{K}$

Or should I do the process some other way?

This may help:

Electric field inside a material​

 

[Steve4Physics]

While writing the comment my mind said, $\vec E_0=\frac{q}{4\pi \vec r^2 \epsilon_0}$

That's the field a distance r from an isolated point charge (or outside a spherically symmetric charge-distribution where r is the distance to the centre). So the equation is not applicable here.

(Also the left side of the equation is a vector but the right side is a scalar.)