text: The ratio of 1/(4pi epsilon_0) -- the Coulomb constant -- results from nothing more than which unit system you are working in. in some unit systems this fraction is just 1. In the form you present, you're using the MKS system.\n\nthe 4pi is the value of having integrated over all theta from 0 to 2pi and all phi from 0 to pi.\n\nepsilon_0 is the permittivity (aka, dielectric constant, or dielectric function) of free space. Free space is what we think of as being completely empty space. It is also the "base unit" of dielectric values. So, for example, if you have a capacitor with a dielectric material inside, the dielectric constant epsilon might be written as epsilon*epsilon_0 where epsilon itself might be say 4 or 5.5, etc. The dielectric constant can be thought of as nothing more than a "screening parameter". All it does is scale (or screen) the electric field strength within a system (with respect to the "unscreened" values which are obtained in free space -- using epsilon_0)\n\nHere is the value of epsilon_0 (as given by google) Note the units: \nhttp://www.google.com/search?hl=en&lr=&q=epsilon_0\n\n\nAnd here is the Google Calculator operation for the "electrostatic constant": \n\nhttp://www.google.com/search?hl=en&lr=&q=1%2F%284*pi*epsilon_0%29\n\nSo -- it's all about the unit system in which you do a problem. Nothing more. \n\nTry the wolfram database for brief comment: http://scienceworld.wolfram.com/physics/CoulombsConstant.html