Coulombs law in SI system is given by
from where does the factor 4[tex]\pi[/tex] come in.
(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
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.
From the above
..obvious by simple maths, :) but why the ratio between surface area and radius squared...
agree with that, but why the fixation with [itex]4\,\pi[/itex] term in a law.
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.
erm … i was assuming you'd look at the detail near the bottom of the page!
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