When exactly is it useful to use (electricity)

[Elbobo]

When is it more simple to use 1 / (4 pi * permitivity of free space) versus k, the Coulomb constant in electrical force/ electrical field formulas? My teacher and my textbook say there are times when it simplifies things, but I have yet to find any reasoning behind it.

 

[Nabeshin]

They're the same thing. If you calculate it out, they're both approximately 9x10^9. The 1/(4 pi * permittivity of free space) just comes from gauss' law. Coulomb's law was developed earlier (I believe) and so in place of this, a constant was used, k, and its value experimentally calculated.

Also, without having studied gauss' law it doesn't make much sense to write it in the longer form, after all, it is just a constant.

 

[Elbobo]

Well that's what I thought too, but again, my teacher and my Giancoli textbook both say there are times when the calculations become simplied, somehow.

 

[Dr Lots-o'watts]

When using Maxwell's equations, you see permittivity of free space everywhere. There is no use in writing 1/(4 pi k) instead.

 

[Loren Booda]

It seems that k is a constant with little physical significance by itself, but convenient in calculations for its singular value. Permittivity, a physical property, and Gauss's law, representing the geometry of charges, are expressed by the alternative form.

 

[Dadface]

Rationalising the constant ie writing it in the form 1/4 pi epsilon makes a lot of calculations a bit simpler because for many problems the 4 pis will cancel out.Also,epsilon is a fundamental constant and it appears in the equation for the speed of light.I can only think of a few examples where the coulomb constant would be easier one of these being when calculating the force between point charges.As nabeshin pointed out they are the same thing so use whatever form you like.