# Where did the electric constant came from?

1. Dec 20, 2009

### LucasGB

- 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)

2. Dec 20, 2009

### SystemTheory

3. Dec 20, 2009

### LucasGB

4. Dec 20, 2009

### kcdodd

You may find it interesting to study what units actually are. You can start with looking at http://en.wikipedia.org/wiki/Natural_units" [Broken]

Last edited by a moderator: May 4, 2017
5. Dec 20, 2009

### LucasGB

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. Dec 20, 2009

### Born2bwire

The value of "k" isn't chosen solely as a simplification, it is a constant of proportionality. Coulomb's law is simply,

$$\mathbf{F} = k\frac{q_1q_2}{r^2}\hat{r}$$

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. Dec 21, 2009

### LucasGB

So the coulomb came before the epsilon zero? Historically speaking, the definition of the coulomb came before the definition of epsilon zero?

8. Dec 21, 2009

### clem

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. Dec 21, 2009

### Born2bwire

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. Dec 21, 2009

### kowalski

Epsilon zero is absolutely meaningless. Use Gaussian or Heaviside-Lorentz units.

11. Dec 21, 2009

### diazona

Although bear in mind that doing so deprives you of on very useful way to check calculations.

12. Dec 21, 2009

### LucasGB

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. Dec 21, 2009

### diazona

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 $\epsilon_0$ would happen to be equal to 1. As you might guess, this whole unit business is not particularly rigorous.

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 $c$, $\hbar$, 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. Dec 21, 2009

### LucasGB

Beautiful, I understand everything very well now. Thank you all for your help.

15. Dec 21, 2009

### diazona

Cool, glad I could help (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. Dec 21, 2009

### Born2bwire

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. :yuck:

17. Dec 22, 2009

### LucasGB

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?