# Units of q in Electric Field Equation

• I
• Drakkith
C as the value of the electron charge in those units. In SI base units, the electric charge is As (Ampere seconds) from which 1 C = 1 As is derived.f

#### Drakkith

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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?

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.

• tech99
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).

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.

• hutchphd, Drakkith and vanhees71
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")

• vanhees71, Bystander and malawi_glenn
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 and hutchphd
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}## :-).

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

• vanhees71