Help me to understand Coulomb's law.

[sphyics]

Coulombs law in SI system is given by

from where does the factor 4\pi come in.

 

[tiny-tim]

hi sphyics!

(have an epsilon: ε )

it's because 4πε₀r² = ε₀A(r), where A(r) is the surface area of a sphere of radius r

see the pf library on Coulomb's law for more details

 

[Dadface]

Putting it another way you can express the constant as a straightforward k where (k is a constant of the medium) but for many problems 4 pi would appear in the final answer.By expressing the constant as 1/4pi epsilon(which of course is equal to k) the 4 pis would cancel in said problems.Take your choice as to how to express the constant but the 1/4pi epsilon option,although it may look more complicated at first sight,actually works out to be the neater option.

 

[sphyics]

https://www.physicsforums.com/library.php?do=view_item&itemid=114
From the above

...and 4\,\pi is the ratio between the surface area of a sphere and the radius squared.

..obvious by simple maths, :) but why the ratio between surface area and radius squared...

 

[sphyics]

Putting it another way you can express the constant as a straightforward k where (k is a constant of the medium) but for many problems 4 pi would appear in the final answer.By expressing the constant as 1/4pi epsilon(which of course is equal to k) the 4 pis would cancel in said problems.Take your choice as to how to express the constant but the 1/4pi epsilon option,although it may look more complicated at first sight,actually works out to be the neater option.

agree with that, but why the fixation with 4\,\pi term in a law.

 

[Dadface]

The best example I can think of:
The speed of light in a vacuum is given by root 1/epsilon zero* mu zero
epsilon zero is an electrical constant of the vacuum(as you know) and mu zero a magnetic constant of the vacuum.If we expressed the constant in Coulombs law as a straightforward k then the equation giving the speed of light would be a bit busier( with its 4 pi) and arguably less elegant.Expressing the constant with the 4 pi just works out easier for the majority(not all) of the problems we do.

 

[tiny-tim]

https://www.physicsforums.com/library.php?do=view_item&itemid=114
From the above
..obvious by simple maths, :) but why the ratio between surface area and radius squared...

erm … i was assuming you'd look at the detail near the bottom of the page!