Why the force constant in coulomb`s law is equal to 1/4*pi*epsilon?

Question

Why the force constant in coulomb`s law is equal to 1/4*pi*epsilon?

Answer 1

During the development of Electromagnetic theory (MKS system), a unit charge emanates lines of force that pass through an enclosing sphere and the flux per unit Steradian (angular counterpart of area, of 1square radian) was assumed to be 1. This passes through 4pi Steradians. Later, the unit was rationalised (RMKS system of units) as 1unit of flux passing through the sphere (4pi Steradians) of unit area. Accordingly the 'Epsilon' underwent a modification as 'Epsilon/4pi'. Gauss' divergence theorem states and is taken as the standard for the flux lines passing through a volume enclosing a charge. While in the earlier case it is 4pi flux lines, in latter case it is fixed as 1 unit of flux lines.

Answer 2

Well its an experimentally found value of that constant , which gave all the correct results....

Answer 3

we know that "force is directly proportional to q1xq2 and inversely propotional to square of radius(r)

To remove propotionality sign a constant 'K' is introduced.

F=Kq1xq2/square of radius'r'

where K is the Coulomb's constant and its value is

K=1/4*pi*epsilon