# Units of q in Electric Field Equation

• I
• Drakkith
In summary: 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.
Drakkith
Mentor
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?

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).

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.

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

## What are the units of q in the electric field equation?

The units of q in the electric field equation are Coulombs (C). The electric field equation typically takes the form E = k * q / r², where E is the electric field strength, k is Coulomb's constant, q is the charge, and r is the distance from the charge.

## Why is the unit of charge in Coulombs?

The unit of charge is in Coulombs because it is the standard unit of electric charge in the International System of Units (SI). It is named after Charles-Augustin de Coulomb, who formulated Coulomb's law, describing the electrostatic force between electric charges.

## How do you convert between different units of charge?

To convert between different units of charge, you can use the conversion factors. For example, 1 Coulomb (C) is equal to 1,000 milliCoulombs (mC), 1,000,000 microCoulombs (µC), or approximately 6.242 x 10^18 elementary charges (e). These conversions help in dealing with practical quantities of charge in various contexts.

## What is the significance of the charge unit in the electric field equation?

The charge unit in the electric field equation is significant because it determines the magnitude of the electric field produced by a given charge. A larger charge (in Coulombs) will produce a stronger electric field at a given distance, according to the equation E = k * q / r².

## Are there any other common units used for charge in the electric field equation?

While Coulombs (C) are the standard SI unit for charge, other units like milliCoulombs (mC), microCoulombs (µC), and elementary charges (e) are also commonly used, especially in specific scientific contexts or when dealing with very small or very large quantities of charge.

• Electromagnetism
Replies
2
Views
208
• Electromagnetism
Replies
1
Views
218
• Electromagnetism
Replies
25
Views
1K
• Electromagnetism
Replies
3
Views
867
• Electromagnetism
Replies
4
Views
971
• Electromagnetism
Replies
11
Views
402
• Electromagnetism
Replies
22
Views
1K
• Electromagnetism
Replies
130
Views
11K
• Electromagnetism
Replies
8
Views
1K
• Electromagnetism
Replies
51
Views
6K