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.

 

[sardar]

Coulomb's constant, also known as the electrostatic constant, is a fundamental constant in physics that represents the strength of the electrostatic force between two charged particles. It is similar to the gravitational constant, which represents the strength of the gravitational force between two masses.

The reason why Coulomb's constant is written as 1/(4*pi*epsilon0) is due to the nature of the electrostatic force. Unlike gravity, which is a long-range force, the electrostatic force between two charged particles decreases rapidly as the distance between them increases. This is because the force is inversely proportional to the square of the distance between the particles.

To account for this rapid decrease in force with distance, the constant 1/(4*pi) is included in the equation. This value is a result of mathematical calculations and does not have a physical significance. It is simply a way to make the equation more convenient to use and understand.

Additionally, epsilon0 (epsilon naught) is the permittivity of free space, which represents the ability of space to allow the electric field to pass through it. It is a fundamental constant that has been experimentally determined and is necessary to accurately represent the electrostatic force.

In summary, writing Coulomb's constant as 1/(4*pi*epsilon0) is a way to account for the rapid decrease in force with distance and to accurately represent the electrostatic force between two charged particles. It is not a complex way of writing the constant, but rather a necessary and accurate representation of the physical phenomenon.