Permittivity Constant and Coulomb's Law

In summary, the use of \frac{1}{4\pi\epsilon_{0}} in place of the usual value for K in Coulomb's law is a somewhat more complicated way that can make future equations easier. While \frac{1}{4\pi\epsilon_{0}} is used in equations, the value for K is typically used when calculating the final answer. This is due to convenience and a stigma of unprofessionalism when only using K. The use of \frac{1}{4\pi\epsilon_{0}} may also come into play later when discussing Gauss' law.
  • #1
erok81
464
0
This is more of a general question than a homework problem.

We haven't gotten too far into e&m so maybe there is a different use for this later on that I just haven't seen yet. Even skipping 7-8 chapters ahead, it is still used in the same way.

What is the point of using [tex]\frac{1}{4\pi\epsilon_{0}}[/tex] in place of the usual value for K? The only detail my textbook has gone into it is "It turns out we can make many future equations easier if we rewrite Coulomb's law in a somewhat more complicated way."

Two chapters later we are still writing [tex]\frac{1}{4\pi\epsilon_{0}}[/tex] in the equations, but using the value for K when the final answer is calculated.

So if K = [tex]\frac{1}{4\pi\epsilon_{0}}[/tex], why not just use K?

I'm not arguing why to use K instead of the more complicated version, but more to understand why and when it will come into play later.
 
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  • #2
the [tex] \frac{1}{4\pi\epsilon_{0}} [/tex] is somewhat insightful in light of geometrical interests that you'll certainly talk about what you learn gauss' law (which you can use to derive that constant). At the same time, when you're solving a problem you're generally looking for something more interesting than just the constants out front---so its easier to just write a k.

It's all just convenience issues... there's also a stigma of unprofessionalism when writing just k, I think that's often a big part of it.
 

Related to Permittivity Constant and Coulomb's Law

1. What is the permittivity constant?

The permittivity constant, also known as the electric constant or vacuum permittivity, is a fundamental physical constant that represents the ability of a material to store electrical energy in an electric field. It is denoted by the symbol ε₀ and has a value of approximately 8.85 x 10⁻¹² F/m.

2. How is the permittivity constant related to Coulomb's law?

Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The permittivity constant is included in this equation to account for the influence of the medium in which the charges are located. It is used to calculate the electric force between charged particles in a medium other than a vacuum.

3. What is the difference between permittivity constant and permittivity?

Permittivity and permittivity constant are often used interchangeably, but they are not the same thing. Permittivity refers to the ability of a material to store electrical energy in an electric field, while the permittivity constant is a numerical value that represents this ability. Permittivity is dependent on the material, while the permittivity constant is a universal physical constant.

4. How does the permittivity constant vary in different materials?

The permittivity constant varies in different materials depending on their ability to store electrical energy. In general, materials with high permittivity constants have a greater ability to store electrical energy and are considered good insulators, while materials with low permittivity constants are better conductors of electricity.

5. Can the permittivity constant be changed?

No, the permittivity constant is a fundamental physical constant and cannot be changed. However, the permittivity of a material can be altered by changing its physical properties, such as temperature or pressure. This will in turn affect the permittivity constant for that particular material in that specific condition.

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