Units of q in Electric Field Equation

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Discussion Overview

The discussion revolves around the units of charge (denoted as ##q##) in the context of the electric field equation, specifically comparing SI and cgs units. Participants explore the implications of different unit systems on the formulation of the electric field and related concepts.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions whether the unit of charge ##q## in the electric field equation is Coulombs, suggesting that it may depend on the units used for calculating electric force.
  • Another participant confirms that in SI units, charge ##q## is indeed measured in Coulombs, while noting that other unit systems exist.
  • A participant asks how the electric field equation changes when using cgs units.
  • It is noted that in cgs units, the unit of charge is the electrostatic unit (esu), and the constant in Coulomb's law is set to 1, leading to specific force interactions between charges.
  • One participant explains that in SI base units, electric charge can also be expressed as Ampere seconds (As), clarifying the relationship between Coulombs and As.
  • A participant shares a personal anecdote about confusion regarding the unit of charge, initially thinking it was based on elementary charge units, which led to issues in programming.
  • Another participant provides the value of charge for an electron, indicating that today the elementary charge ##e## is defined to establish the base unit of charge, Coulombs.
  • One participant reiterates the cgs unit of charge and presents the electric field equation in Gaussian units, emphasizing the absence of the ##1/4\pi e_0## factor.
  • A recommendation is made for a book chapter that discusses systems of units, humorously suggesting it should address the placement of ##4\pi## factors.
  • Another participant humorously agrees with the title suggestion regarding the ##4\pi## factors.
  • A participant mentions Heaviside-Lorentz units, noting their advantages in terms of unit consistency for electric and magnetic field components.
  • One participant comments on the memorization required for using different unit systems, particularly the number 1 in the context of alternative units.

Areas of Agreement / Disagreement

Participants generally agree on the definitions of charge in SI and cgs units, but there are multiple competing views regarding the implications of different unit systems and the relevance of the ##4\pi## factors in equations. The discussion remains unresolved regarding the best approach to unit systems.

Contextual Notes

Some participants express uncertainty about the implications of using different unit systems, and there are references to specific constants and their roles in various formulations, which may depend on the context of the discussion.

Drakkith
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TL;DR
What Are the Units of q in the EField Equation?
Quick and possibly stupid question, but in the equation for calculating the electric field:
##{\mathbf E} = \frac{1}{4πe_0}\frac{q}{r^2} \hat {\mathbf r}##

What unit is ##q## in? Coulombs?
Although now that I think more on it I suppose it also depends on the units you're using to calculate the electric force on a charged particle, correct?
 
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In SI, the unit of charge ##q## is Coulombs. There are other units for other systems.
 
How does the above equation change if we move to, say, cgs units?
 
In cgs the unit of charge is the electrostatic unit, or esu. The constant in Coulombs law is set equal to 1. Therefore, two charges each with charge 1 esu sitting 1 cm apart will feel a force between them of 1 dyne.
 
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Note that in SI base units, the electric charge is As (Ampere seconds) from which 1 C = 1 As is derived.
 
Thanks all. For some reason I was thinking ##q## was in units of single electron/proton charges and I was in a rabbit hole of debugging my program because I thought it was acting wonky. No, I just didn't need to enter 1e20 for the amount of charge...
 
For an electron ##q=-e \simeq -1.6 \cdot 10^{-19} \text{C}##. Note that today ##e## is fixed by definition, i.e., it's used to define the base unit of charge, C (or for historical reasons rather of current, A).
 
gneill said:
In cgs the unit of charge is the electrostatic unit, or esu. The constant in Coulombs law is set equal to 1. Therefore, two charges each with charge 1 esu sitting 1 cm apart will feel a force between them of 1 dyne.
To complement this answer, this means that the equation for the electric field in Gaussian units (cgs) is
$${\mathbf E} = \frac{q}{r^2} \hat {\mathbf r}$$
The factor ##1/4πe_0## is an artefact of the SI system of units.
 
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I recommend a chapter in Wangsness book, titled "Systems of Units: A Guide to the Perplexed."

It should be titled "Where do the 4πs go")
 
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Vanadium 50 said:
It should be titled "Where do the 4πs go")
Give me a Ψ and I'll show you.

Get it? Because it's shaped like a fork?
 
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  • #11
Heaviside-Lorentz units rule! There you've the factors of ##4 \pi## at the right places and no idiosyncratic different units for the field components ##\vec{E}## and ##\vec{B}## :-).
 
  • #12
The problem with the 'other' units is that you have to memorize the number 1.
 
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