Question

In the Lecture 1: What holds our world together
The 4pi epsilon 0 appears as due to historical reason.

Is anybody knows the reason why the 4Pi has appeared in the fomula ?

F=(q1 x q2) x K / r²
K=1/4Pi Epsilon0

Answer 1

The constant K is an empirical constant. It is merely added to make the relation between the force and the mentioned parameters accurate and universal for all cases of study. Obviously when we use the constants, we should get the same value for all cases of study. For example, we can measure the force between two charges q1 and q2 for a particular distance and change the distance and again measure it, if we compare the both, we can find that they only vary with the distance which has been changed. So this constant K is really our choice. By definition, if we use unit charges and unit distance separating them, the force is given as 1/4piEo which can be verified experimentally.

Also another way to justify this is if force is in newtons, charge is in coulombs and distance is in meters, the SI system has the value of 1/4piEo for this constant K

Answer 2

Thank you for your answer.
Nevertheless I m not fully satisfied with the answer (or I may not as ask the question clearly).

I can't imagine that (but I may be wrong), the 4pi appears only without any reason...
Ok I understand that K=1/4piEo by the way given to the Eo the value associated to that relation
But there must be a rational for which we choose K=1/4piEo and not K=1/2piEo (with another value of Eo) or whatever...

There must be an explanation.

The 4pi in "K=1/4piEo" certainly appears in order to remove 4pi in a results where K appears...

X=K*4pi Y and then they should have decided to introduce a new variable Eo as (K=1/4piEo) in order to remove the 4pi
hence : X=1/Eo Y
More easy to use than X=K*4pi Y

Just a suggestion...

Answer 3

yes, its completely relative as such. I have already mentioned that the experimental results complied with this accepted value for K. I mean they simply must have measured the force for various charges and distances between them and found out that all of these varied with a common factor 1/4piEo which is the reason why it appears as the proportionality constant. Also if we take the charges to be 1C and distance to be 1m, the force between them is given as 1/4piEo and not 1/2piEo. This is why they take the constant as 1/4piEo.

Eo is a constant which is the absolute permitivity or permitivity of free space. These are fixed constants just like the Universal gravitational constant and hence as a convention we settle for these specific values.

Please refer to the historical origins of Eo in the link given below for a further reference.

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

Answer 4

Surface Area of a Sphere \(=4πr^2\)

Answer 5

It can be seen as a result of Gauss law on a point-charge

Answer 6

I feel its this way

so you see.. they found out that the force does depend upon the medium in which the charges are present.. Hence now they need to know how does that force vary with the medium.. there must be some way in which we can represent how the force varies with the medium

hence the constant K.. has to be somehow related to property of the medium that affects the electric force.. that property was already defined to be permittivity.. and permittivity value is also well defined ..

so now all we need to do is.. get the math right.. so i can write K in terms of permittivity.. so 4pi is the factor that makes it right.. tada!

Answer 7

\[\oint_S\vec E\cdot \mathrm dA=\frac Q\varepsilon_0\\\vec E \cdot 4\pi r^2\hat{\mathbf r}=\frac Q\varepsilon_0\\\vec E=\frac{Q}{4\pi \varepsilon_0r^2}\hat{\mathbf r}\\\vec F=\frac{qQ}{4\pi \varepsilon_0r^2}\hat{\mathbf r}\]

Answer 8

i am having the same question in mind....the constant of proportionality in case of magnetism is\[\mu _{0}\]its value is \[4\pi*10^{-7}\]....again the inverse of the product of \[\mu _{0}] & [\epsilon _{0} \] is the square of velocity of light....