# Electric field using dielectric constant

• Issy
In summary: My school didn't have a "physics" degree - it was a BS in "physical sciences" with a concentration in physics.In summary, the conversation is about finding the magnitude of the electric field due to a charge located underwater using the equation E = kq/r^2, where k is the constant 9 x 10^9 and q is the charge. The dielectric constant, or kappa, is also used in this equation for different environments. The use of Gauss's law and a gaussian surface is also recommended for more complex situations involving charges and dielectric materials.
Issy

## Homework Statement

What is the magnitude of the electric field due to a 6.0 x 10-9 C charge at a point located 0.025m from the charge? The charge and the point in question are located underwater (κ(water) = 80).

## Homework Equations

I know that E = magnitude of electric field = kq/r2, where k = Coulomb's constant of 9 x 109, and I also know that κ = kappa = dielectric constant aka relative permittivity of a dielectric material, which we use in the equation C = capacitance = κεoA/d.

However, I can't workout how to use κ to find electric field strength, because I don't see how a capacitor is involved in this situation? And with the three variables I have been given (the size and electric polarity of charge, the distance, and the dielectric constant of water), I also don't know of any formulas I can use that don't require any other variables.

The practise test I'm working on is multichoice, and the answers state that the final answer is equal to 1.1 x 103 N/C, but I'm not sure how to work backwards from that either. Any help would be greatly appreciated! We have a test later this week, and I'm sure Murphy's Law will make sure that unless I get my head around it, a question like this will no doubt be in the exam, so any and all advice will be welcomed!

use this equation E=Kq/kr^2,where

K= 9 * 10^9
k=dielectric constant
q=charge
r=distance in question

Edit: Answer is 1.08 * 10^3 N/C

Equation reference: H C Verma Concepts Of Physics

Last edited:
Issy
Do you need any proof of this equation?

ash64449 said:
use this equation E=Kq/kr^2,where

K= 9 * 10^9
k=dielectric constant
q=charge
r=distance in question

Edit: Answer is 1.08 * 10^3 N/C

Equation reference: H C Verma Concepts Of Physics
Thank you very much! So, is it fair to say that dielectric constant (ie Kappa) is actually always used in the E=kq/r2 equation when the surrounding environment is not specified? Which would mean it's assumed that it's just air, which has a dielectric constant of 1, so doesn't actually affect the equation?
...I guess what I'm asking, in a roundabout way, is should I use that equation for any question where the surrounding environment of the charge is not air?
Thank you again for your help, I had no idea how to approach it, you've saved me a lot of confusion!

Issy said:
Thank you very much! So, is it fair to say that dielectric constant (ie Kappa) is actually always used in the E=kq/r2 equation when the surrounding environment is not specified? Which would mean it's assumed that it's just air, which has a dielectric constant of 1, so doesn't actually affect the equation?
...I guess what I'm asking, in a roundabout way, is should I use that equation for any question where the surrounding environment of the charge is not air?
Thank you again for your help, I had no idea how to approach it, you've saved me a lot of confusion!

Yes.. You are right! Thank you! you are welcome!

Issy
There is one thing that you should know... Once you use kappa in the equation.. you should never use the bound charge appearing due to polarization of the dielectric.

only free charge should be used..

Use a gaussian surface around your charge, and Gauss's law.
Now you can handle any combination of charge and observation point being surrounded by various dielectric material.
.

Issy
rude man said:
Use a gaussian surface around your charge, and Gauss's law.
Now you can handle any combination of charge and observation point being surrounded by various dielectric material.
.
I'm going to bookmark this thread, because while I currently have no idea about Gauss' Law, no doubt I'll find out about it next semester, or soon enough. Thank you for your advice! Sometimes it seems like every time I learn a new physics concept, I become aware of half a dozen others that I also need to learn - but it makes my degree more entertaining if I think of it as fighting a Hydra! Thank you again

mooncrater
The constant K we use in finding the electric field is= $$\frac {1}{4\pi \epsilon_0}$$
So , when you are talking about an dielectric just replace the ##\epsilon_0## part with ##k\epsilon_0## where k is the dielectric constant , just the way you do for the capacitors. Thats why you get that k in the denomimator of the formula.

Issy said:
I'm going to bookmark this thread, because while I currently have no idea about Gauss' Law, no doubt I'll find out about it next semester, or soon enough. Thank you for your advice! Sometimes it seems like every time I learn a new physics concept, I become aware of half a dozen others that I also need to learn - but it makes my degree more entertaining if I think of it as fighting a Hydra! Thank you again
Har! Are you going for a physics major or something like "physical sciences" where calculus-level physics is not covered? My school had that option & most others do too I'm sure. So you may or may not run into Dr. Gauss.

## 1. What is the dielectric constant?

The dielectric constant, also known as the relative permittivity, is a measure of how well a material can store electrical energy in an electric field. It is the ratio of the electric flux density in a vacuum to the electric flux density in the material.

## 2. How does the dielectric constant affect the electric field?

The dielectric constant affects the electric field by reducing the strength of the electric field in a material. This is because the presence of a dielectric material reduces the amount of charge that can build up on the surface of a conductor, resulting in a weaker electric field.

## 3. What is the relationship between the dielectric constant and capacitance?

The dielectric constant and capacitance are directly proportional to each other. This means that as the dielectric constant increases, the capacitance also increases. This is because a higher dielectric constant means that a material can store more electrical energy, resulting in a higher capacitance.

## 4. How is the dielectric constant measured?

The dielectric constant can be measured using a device called a capacitance meter. This device measures the capacitance of a material and uses it to calculate the dielectric constant. It can also be calculated using the dimensions and properties of a material, such as its permittivity and thickness.

## 5. What are some common materials with high and low dielectric constants?

Some common materials with high dielectric constants include water, ceramic materials, and most types of plastics. Materials with low dielectric constants include air, vacuum, and certain types of gases. The dielectric constant of a material also varies with temperature and can be altered by adding impurities or changing its physical structure.

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