When exactly is it useful to use (electricity)

  • Context: Undergrad 
  • Thread starter Thread starter Elbobo
  • Start date Start date
  • Tags Tags
    Electricity
Click For Summary

Discussion Overview

The discussion revolves around the use of the expression 1 / (4 pi * permittivity of free space) versus the Coulomb constant (k) in electrical force and field formulas. Participants explore when one form may simplify calculations compared to the other, touching on theoretical and practical implications.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that both expressions yield approximately the same numerical value, around 9x10^9, and suggest that 1/(4 pi * permittivity of free space) derives from Gauss's law.
  • Others argue that the Coulomb constant (k) is more convenient for calculations involving point charges, while the permittivity form is more prevalent in Maxwell's equations.
  • One participant highlights that using the permittivity form can simplify calculations as the 4 pi terms often cancel out in various problems.
  • There is mention of the physical significance of permittivity as a fundamental constant, contrasting it with k, which some view as having less physical significance on its own.
  • Participants express uncertainty about the specific scenarios where one form is preferred over the other, referencing guidance from textbooks and teachers without reaching a consensus.

Areas of Agreement / Disagreement

Participants generally agree that both forms are equivalent in value, but there is no consensus on when one form is definitively more useful than the other. Multiple competing views remain regarding their applications and significance.

Contextual Notes

Some assumptions about the context of use for each expression are not fully explored, and the discussion does not resolve the specific conditions under which one form may simplify calculations more than the other.

Elbobo
Messages
145
Reaction score
0
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.
 
Physics news on Phys.org
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.
 
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.
 
When using Maxwell's equations, you see permittivity of free space everywhere. There is no use in writing 1/(4 pi k) instead.
 
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.
 
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.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 4 ·
Replies
4
Views
5K
  • · Replies 25 ·
Replies
25
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K