- #1

Istiak

- 158

- 12

- 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?