# Understanding Coulomb's Force Equation in Free Space: Exploring Permittivity

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• pranav p v
In summary: No, you would not. Permittivity and permeability are not related to the velocity of light in the same way as charge and mass are.
pranav p v
I have a doubt about coulomb's force equation in free space..ie 1/4πε0... Actually coulomb found that force exerted b/w charges are directly proportional to the product of charges and inversely proportional to the sqr of the distance bw them.we can measure force exerted and distance of separation but that was the first time to quantify how much charges are there...so we can choose any value to that charges..by taking proprtionality constant as 1 we can write the equation as f= q1q2/r²..so 1 unit of charge can be defined as amount of similar 2 charges when they are separated by 1 unit exerted 1 unit of force..

but inorder to simplify gauss's law equation we can put proportionality constant as 1/4π and also we can define 1 unit of charge accordingly..
but why we include 1/ε0 term in the equation..i know that force will be different for different medium of separation..so we can include a term which have different values for different material ( relative Permittivity)... My question is why don't we chose ε0 as 1 ?(εr can be included but why we choose ε0 as strange value) .give the answer please...

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Dale
But how to get the value of ε0 as 8.85*10^-12 by converting heaviside-lorentz units into si unit?? In HLU mass is in gram , length in cm time in s.if we convert that units into kg,m then we will get the factor of 10^-9...so that unit of charge is not same for both...can u derive the value of ε0 mathematically by converting HLU to SI units?? Up to HLU system i am ok.please reply

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pranav p v said:

Plz uze reel wurdz,

I have no idea what you are talking about. Take a few minutes, and repost what you are misunderstanding. If you use proper English, we are less likely to misunderstand as well.

pranav p v said:
so that unit of charge is not same for both
That is correct, the unit of charge is not the same for both

pranav p v said:
can u derive the value of ε0 mathematically by converting HLU to SI units?
No. You cannot derive any system of units by converting it. Units are human conventions. Their values are decided by people. In the case of SI units by the BIPM committee. The BIPM took a vote and decided how big to make the ampere and the mechanical units, and the constant followed from that arbitrary decision.

pranav p v said:
if we convert that units into kg,m then we will get the factor of 10^-9...so that unit of charge is not same for both
Indeed the unit of charge is different in the two systems of units. The charge on e.g. an electron has different numerical values, depending on the units used.

If you consider e.g. two electrons 1.00 m (100 cm) apart, you should get the same electric force between them, regardless of the system of units, provided you use the appropriate form of Coulomb's Law in each system. If you don't, then show your calculations and someone can probably comment on them.

Dale said:
That is correct, the unit of charge is not the same for both

No. You cannot derive any system of units by converting it. Units are human conventions. Their values are decided by people. In the case of SI units by the BIPM committee. The BIPM took a vote and decided how big to make the ampere and the mechanical units, and the constant followed from that arbitrary decision.

Sir..but why did they choose a strange number as Permittivity? Even though in SI system we can use Permittivity as unity ( like in HLU) that makes equation simpler. By this we can define one coulomb of charge accordingly.there would be a specific reason for this strange value, right?
I know there's a relationship between Permittivity, permeability and speed of light..but that relation can be obtained only from wave equation..if i choose Permittivity and permeability as unity then don't i get velocity of light as 3*10^8 m/s?? Will it be also unity??

pranav p v said:
why did they choose a strange number as Permittivity?
You can look up the history on the Wikipedia entry for the ampere. They chose a convenient size of the magnetic force between two wires, and so the constant wound up being strange.

pranav p v said:
Even though in SI system we can use Permittivity as unity
Well, you couldn't do that in SI units, it would be a different system of units. Heaviside Lorenz units is a different system of units.

pranav p v said:
if i choose Permittivity and permeability as unity then don't i get velocity of light as 3*10^8 m/s?? Will it be also unity??
Yes. That approach is taken with Planck units and other similar systems of "natural units"

If you look at many threads in our Relativity forum, you'll see many people using units in which c = 1 (e.g. 1 light-year per year), to make calculations simpler in examples and exercises!

Sir,
So permeability was defined before Permittivity?
From ampere's force per unit length f∝i*i/r
In cgs system they chose proportionality constant as 2( i don't know why)
So f per length=2ii/r
Inorder to simplify ampere's law 1/2π was included but they chose same unit of current in the SI system so 2π should be multiplied in the numerator also.and there will be a factor of 10^-7 in the numerator by converting cm to m ang g to kg...so permeability is 2*2π*10^-7=4π*10^-7... Maxwell had proven that light is an electromagnetic wave .and speed of light is inter related by the constant of proprtionalities of Coulomb's law ( not included 4pi,or constant in gauss's law ie ε0) and ampere's circuital law( ie μ0.). so value of ε0 was chosen by the realtion ε0 =1/(μ0c²)...
Is it correct?
If yes then which was the system of unit followed by James clerk Maxwell? If we use HLU then speed of EM wave will be 1.. then how can we say light is EM wave?... what was the unit of velocity of wave he obtained?

pranav p v said:
If yes then which was the system of unit followed by James clerk Maxwell? If we use HLU then speed of EM wave will be 1.. then how can we say light is EM wave?... what was the unit of velocity of wave he obtained?
He made experiments to ascertain the ratio of electromagnetic to electrostatic units, and applied this number to his physical analogy, which used a system of rotating cells. The model was then found to transmit waves at 288,000 km/s. ("The Man who Changed Everything", by Basil Mahon, Wiley).

pranav p v said:
Maxwell had proven that light is an electromagnetic wave .and speed of light is inter related by the constant of proprtionalities of Coulomb's law ( not included 4pi,or constant in gauss's law ie ε0) and ampere's circuital law( ie μ0.). so value of ε0 was chosen by the realtion ε0 =1/(μ0c²)...
Is it correct?
No, in effect the values of ##\varepsilon_0## and ##\mu_0## had already been determined experimentally, when Maxwell came up with the equivalent of ##c = 1 / \sqrt{\varepsilon_0 \mu_0}## for the speed of his electromagnetic waves. He plugged those values into the equation to predict the speed of electromagnetic waves, and noted that that speed was very close to recent experimental measurements of the speed of light.

I say "in effect" and "equivalent" because Maxwell used different notation, terminology and units than what we use nowadays. You can see his actual numbers here:

https://en.wikisource.org/wiki/Page:Philosophical_magazine_23_series_4.djvu/38

where equation 136 gives his prediction for the speed of electromagnetic waves, and equation 137 gives the measured value of the speed of light.

cnh1995 and Dale

## 1. What is Coulomb's Force Equation?

Coulomb's Force Equation, also known as the Law of Electrostatics, is an equation that describes the force between two charged particles in a vacuum or free space. It is represented as F = k(q1q2)/r^2, where F is the force, k is the Coulomb's constant, q1 and q2 are the charges of the particles, and r is the distance between them.

## 2. What is permittivity?

Permittivity is a measure of a material's ability to store an electric charge. It is represented by the symbol ε and is measured in units of farads per meter (F/m). It determines how much electric flux is generated by a given amount of electric field in a material.

## 3. How is permittivity related to Coulomb's Force Equation?

Permittivity is an important factor in Coulomb's Force Equation as it determines the strength of the electric field between two charged particles. The higher the permittivity of the material between the particles, the stronger the force will be between them.

## 4. What is the significance of exploring permittivity in free space?

Exploring permittivity in free space allows us to understand the behavior of charged particles without the influence of any external materials. This is important in many scientific and technological applications, such as in the design of electronic devices and understanding the behavior of particles in outer space.

## 5. How does the distance between two charged particles affect Coulomb's Force Equation?

The distance between two charged particles is an inverse square relationship in Coulomb's Force Equation. This means that as the distance between the particles increases, the force between them decreases exponentially. This relationship is crucial in understanding the behavior of charged particles and designing experiments and technologies that involve electric fields.

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