Why is Coulombs Constant Written as 1/(4*pi*epsilon0)?

[salmannsu]

q: why we express coulomb constant constant in 1/(4*pi*epsilon0) form rather writing as a constant value 9*10^9 ?
why we do not write the value directly as a gravitational constant

why 1/(4*pi) came with the constant, we can directly write the exact value.

whats the benefit of writing in this complex way..please help. i am looking for your help

 

[nicksauce]

Because then we have in Maxwell's equations we have the nice form
\nabla\cdot\vec{E} = \frac{\rho}{\epsilon_0}

 

[salmannsu]

That is a cool Answer. but why we do that it is not really clear to me . Because coulombs law was suggested much more earlier that Gauses law and Maxwell equation. So why we changes in coulombs law rather changing Maxwell equation. Is there any significance ?

 

[pgardn]

That is a cool Answer. but why we do that it is not really clear to me . Because coulombs law was suggested much more earlier that Gauses law and Maxwell equation. So why we changes in coulombs law rather changing Maxwell equation. Is there any significance ?

It is a useful way to express the empirical number of ~9 x 10^9 due to the geometry required to understand and describe some simple electric fields. Many electric fields are incredibly complex but those that show spherical symmetry can be described. If one starts using Gauss, and the spherical symmetry required to use Gauss effectively, pi shows up. If you express k in terms of pi you can make the equations look a little nicer because pi pops up and you can cancel it out instead of having to write k with pi in the equation.

Using Gauss and Coulomb for the e-field around a particle it becomes clear that Gauss would require a spherical surface and the total flux would be E.dA and the area of a sphere is 4*pi*r^2. This makes the use of k in terms of 4*pi nice.

Bottom line. It makes things look a little nicer. There are some other complexities involving epsilon, but what I gave you above is what I have gathered after doing problems.