 #1
Istiak
 158
 10
 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?
##\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?