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Rats_N_Cats
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Why the 4π in Coulomb's Law, SI version? The CGS version does well without it...
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Pythagorean said:http://en.wikipedia.org/wiki/Statcoulomb
They're not dimensionally equivalent. The 4pi is a result of the spherical geometry of the field created by a point charge.
In Coulomb's Law, 4π represents the constant of proportionality that relates the electric force between two point charges to their distance and magnitude. It is derived from the surface area of a sphere with a radius equivalent to the distance between the two charges.
The use of 4π in Coulomb's Law is a result of the symmetry of the electric field. The electric field lines emanate outward from a point charge in all directions, creating a spherical shape. Since the electric field is inversely proportional to the square of the distance between charges, the constant of proportionality must be 4π in order to maintain this symmetry.
No, 4π is a fundamental constant that cannot be replaced with another value in Coulomb's Law. It is a result of the geometry and symmetry involved in the electric field between two point charges.
While 4π is a necessary constant in Coulomb's Law, it does not have any physical significance beyond being a mathematical representation of the electric field's symmetry. It does not have any units and is simply a numerical value used in calculations.
The value of 4π was determined through experiments and observations of the electric field between two point charges. The inverse-square law, which states that the strength of the electric field is inversely proportional to the square of the distance between charges, was found to be true for all points on a spherical surface with a radius equivalent to the distance between the charges. This led to the conclusion that the constant of proportionality must be 4π in order to maintain this symmetry.