Where did the electric constant came from?

In summary, Coulomb's Law involves the constant 1/4 pi epsilon zero, which was chosen to simplify calculations. The factor of 4 pi was added to incorporate rationalization and make calculations involving spheres easier. Epsilon zero was added to the constant to match units and magnitudes in the equation. However, some physicists use different unit systems and do not include epsilon zero in their calculations. Overall, the choice of unit system varies depending on the field of physics being studied.
  • #1
LucasGB
181
0
- In Coulomb's Law, 1/4 pi epsilon zero is called Coulomb's Constant. This constant was arbitrarily chosen to simplify calculations.

- The "4 pi" was added to the denominator so situations involving spheres could be simplified (both the formulas for the volume and the surface area of a sphere contain the term "4 pi" in the numerator)

But why was epsilon zero added to the constant? What does it simplify?


(You might find the answer here, I sure as hell didn't: http://en.wikipedia.org/wiki/Electric_constant#Rationalization_of_units)
 
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  • #3
SystemTheory said:
Try this link. It looks like a factor to make units match:

http://en.wikipedia.org/wiki/Vacuum_permittivity

Well, it's actually the same link I posted, but thank you anyway. :smile:
 
  • #4
You may find it interesting to study what units actually are. You can start with looking at http://en.wikipedia.org/wiki/Natural_units"
 
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  • #5
I'm sorry, but I still don't understand. I realize that if the units didn't match, a constant would have to be introduced into the equation. But from what I understand, the unit of charge is what hadn't been established yet, and after the constant was established, the unit of charge was created to make the dimensions right. So, could someone please explain why was the electric constant epsilon zero introduced into Coulomb's Constant?
 
  • #6
The value of "k" isn't chosen solely as a simplification, it is a constant of proportionality. Coulomb's law is simply,

[tex]\mathbf{F} = k\frac{q_1q_2}{r^2}\hat{r}[/tex]

Whatever we choose k to be is dependent upon our chose of units. The factor of 4\pi is the incorporation of rationalization. Somewhere in Maxwell's equations that define electrodynamics you need to have 4\pi. Rationalized units move the 4\pi onto the Coulomb's Law and allows us to remove it from Maxwell's equations. Non-rationalized units place the 4\pi factor in Maxwell's equations and remove it from Coulomb's law. Whatever historical reasons for doing so are probably more or less irrelevant for today. These days it more or less is dictated by whatever convention you feel is easier to deal with. Rationalization aside, the remaining factor in k still needs to match up your units properly since 4\pi is unitless. You could still choose k to be unity, with or without rationalization and you would have Heaviside-Lorentz CGS and Guassian CGS systems of units respectively. But to match it up with SI, or MKS, system, we need to use the MKS \epsilon_0 factor.
 
  • #7
So the coulomb came before the epsilon zero? Historically speaking, the definition of the coulomb came before the definition of epsilon zero?
 
  • #8
epsilonzero was tacked on after everything by people who did not understand the physics. It was finally adopted at an international congress in the 1950's when engineers packed the house and outvoted the physicists. In our own work, most physicists use gaussian or natural units, each having no epsilonzero. We have to teach the elementary courses with epsilon zero and muzero because more engineers take these courses than physicists.
We lie about fourpiepslonzero making things easier. Is it easier to remember fourpiepslonzero or one?
 
  • #9
clem said:
epsilonzero was tacked on after everything by people who did not understand the physics. It was finally adopted at an international congress in the 1950's when engineers packed the house and outvoted the physicists. In our own work, most physicists use gaussian or natural units, each having no epsilonzero. We have to teach the elementary courses with epsilon zero and muzero because more engineers take these courses than physicists.
We lie about fourpiepslonzero making things easier. Is it easier to remember fourpiepslonzero or one?

Sounds like somebody is a little bitter about being brought up to speed with how the rest of the world works with meters, kilograms, and seconds.
 
  • #10
Epsilon zero is absolutely meaningless. Use Gaussian or Heaviside-Lorentz units.
 
  • #11
Although bear in mind that doing so deprives you of on very useful way to check calculations.
 
  • #12
OK, so let me see if I understand. Please correct me if I'm wrong.

- When working with SI units, 4pi is introduced into Coulomb's Law and some other formulas in order to make 4pi disappear in some of Maxwell's Equations.

- But if the constant is defined as 1/4pi alone, units on both sides of the equation won't match. Therefore, epsilonzero is added to the constant in order to make both units and magnitudes match.

Is this correct?

PS.: I'm teaching myself physics, so I would like to know: if you go through physics journals (not engineering journals) what is the unit system most commonly used by physicists?
 
  • #13
LucasGB said:
OK, so let me see if I understand. Please correct me if I'm wrong.

- When working with SI units, 4pi is introduced into Coulomb's Law and some other formulas in order to make 4pi disappear in some of Maxwell's Equations.

- But if the constant is defined as 1/4pi alone, units on both sides of the equation won't match. Therefore, epsilonzero is added to the constant in order to make both units and magnitudes match.

Is this correct?
Well... yes, if you're working in SI units. But you could design a system of units in which there's no separate unit for charge - that is, you could have the unit for charge just be some combination of length, time, and mass units, in such a way that the value of [itex]\epsilon_0[/itex] would happen to be equal to 1. As you might guess, this whole unit business is not particularly rigorous.

LucasGB said:
PS.: I'm teaching myself physics, so I would like to know: if you go through physics journals (not engineering journals) what is the unit system most commonly used by physicists?
Depends on the type of physics. In high-energy particle physics, most quantities are expressed in terms of gigaelectronvolts (GeV), a unit of energy, and it's understood that you should multiply by factors of [itex]c[/itex], [itex]\hbar[/itex], and other constants as necessary if you want to convert to SI units. In other areas, it varies. For certain applications of condensed matter physics, they even invent unit systems based on the physical system being considered, e.g. if you're doing an experiment with argon, you might use the mass of an argon atom as your mass unit. Part of learning to work in a specific field of physics is getting used to the unit conventions used (and part of learning physics in general is learning not to be tied down to a particular system of units!).
 
  • #14
Beautiful, I understand everything very well now. Thank you all for your help.
 
  • #15
Cool, glad I could help :wink: (Although, for the record: when I said this whole unit business is not particularly rigorous, I meant only with respect to the choice of which unit system to use. Whichever one you pick, it's absolutely critical to use it consistently!)
 
  • #16
diazona said:
Cool, glad I could help :wink: (Although, for the record: when I said this whole unit business is not particularly rigorous, I meant only with respect to the choice of which unit system to use. Whichever one you pick, it's absolutely critical to use it consistently!)

Uggg... tell me about it. My group uses MKS, the references I am using for my latest project are in Gaussian CGS, the paper that I am working off of though is in Heaviside-Lorentz CGS.
 
  • #17
Just to wrap this up. The magnitude of epsilon zero (8.8 times 10^-12) is to make the numbers right, and its unit (F times m^-1) is to make units right?
 

Related to Where did the electric constant came from?

1. Where did the concept of electric constant come from?

The concept of electric constant, also known as the permittivity of free space, originated from the works of physicist Michael Faraday in the 19th century. He observed that the force between two charged objects was inversely proportional to the distance between them and proposed the idea of electric field and its constant.

2. How is the electric constant determined?

The value of electric constant is determined through experimentation and calculation. It is calculated by measuring the force between two charged objects of known charge and distance apart. The value is then used to determine the strength of electric fields.

3. What is the significance of electric constant?

The electric constant plays a crucial role in understanding and describing the behavior of electric fields. It is a fundamental constant in electromagnetism and is used in various equations to calculate the strength and direction of electric fields. It also helps in understanding the behavior of capacitors, which store electrical energy.

4. Is the value of electric constant constant?

Yes, the value of electric constant is considered to be a fundamental constant of nature and is assumed to be constant in all regions of space and time. However, recent studies have suggested that the value of electric constant might vary in extreme conditions such as near black holes or during the early stages of the universe.

5. Can the value of electric constant be changed?

No, the value of electric constant cannot be changed as it is considered to be a fundamental constant. However, it can be modified in different materials, known as the relative permittivity, which affects the strength of electric fields in that material. This is why different materials have different insulation properties and conduct electricity differently.

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