Find electric field inside a material

In summary, the question asks for the magnitude of the electric field inside an infinite slab of insulating material with dielectric constant K and permittivity ##\epsilon = K \epsilon_0##, when placed in a uniform electric field of magnitude ##E_0## perpendicular to its surface. Using the equations ##\vec D=\epsilon\vec E## and ##\oint \vec D\cdot d\vec a=q_{f_{enc}}##, it is found that the magnitude of the electric field inside the material is given by ##\vec E= \frac{\vec E_0}{K}##. This is different from the equation for the electric field outside a point charge, ##\vec E_0=\
  • #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?
 
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  • #2
Istiakshovon said:
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

 
  • #3
Istiakshovon said:
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.)
 

1. What is the electric field inside a material?

The electric field inside a material is a measure of the force exerted on a charged particle within the material. It is typically represented by the symbol E and is measured in units of volts per meter (V/m).

2. How is the electric field inside a material calculated?

The electric field inside a material can be calculated using the formula E = V/d, where V is the potential difference across the material and d is the distance between the two points where the potential difference is measured.

3. Does the electric field inside a material vary depending on the type of material?

Yes, the electric field inside a material can vary depending on the type of material. Different materials have different electrical properties, such as conductivity and permittivity, which can affect the strength of the electric field inside the material.

4. Can the electric field inside a material be influenced by external factors?

Yes, the electric field inside a material can be influenced by external factors such as the presence of other charged particles or the application of an external electric field. These external factors can alter the distribution of charges within the material, resulting in a change in the electric field inside.

5. How does the electric field inside a material affect the movement of charged particles?

The electric field inside a material plays a crucial role in determining the movement of charged particles within the material. Charged particles will experience a force in the direction of the electric field, causing them to move in that direction. The strength and direction of the electric field inside a material can impact the speed and trajectory of charged particles within it.

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