Permittivity Constant and Coulomb's Law

[erok81]

This is more of a general question than a homework problem.

We haven't gotten too far into e&m so maybe there is a different use for this later on that I just haven't seen yet. Even skipping 7-8 chapters ahead, it is still used in the same way.

What is the point of using \frac{1}{4\pi\epsilon_{0}} in place of the usual value for K? The only detail my textbook has gone into it is "It turns out we can make many future equations easier if we rewrite Coulomb's law in a somewhat more complicated way."

Two chapters later we are still writing \frac{1}{4\pi\epsilon_{0}} in the equations, but using the value for K when the final answer is calculated.

So if K = \frac{1}{4\pi\epsilon_{0}}, why not just use K?

I'm not arguing why to use K instead of the more complicated version, but more to understand why and when it will come into play later.

 

[zhermes]

the \frac{1}{4\pi\epsilon_{0}} is somewhat insightful in light of geometrical interests that you'll certainly talk about what you learn gauss' law (which you can use to derive that constant). At the same time, when you're solving a problem you're generally looking for something more interesting than just the constants out front---so its easier to just write a k.

It's all just convenience issues... there's also a stigma of unprofessionalism when writing just k, I think that's often a big part of it.