Units of q in Electric Field Equation

[Drakkith]

TL;DR Summary

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?

 

[gneill]

In SI, the unit of charge $q$ is Coulombs. There are other units for other systems.

 

[Drakkith]

How does the above equation change if we move to, say, cgs units?

 

[gneill]

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.

 

[malawi_glenn]

Note that in SI base units, the electric charge is As (Ampere seconds) from which 1 C = 1 As is derived.

 

[Drakkith]

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...

 

[vanhees71]

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).

 

[DrClaude]

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.

 

[Vanadium 50]

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")

 

[Drakkith]

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?

 

[vanhees71]

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 $\vec{B}$ :-).

 

[Meir Achuz]

The problem with the 'other' units is that you have to memorize the number 1.