# Unconvincing sentence in wikipedia

I'm studying about electric field and referring to an article about electric field in wikipedia

And in here, there are some doubtful sentences:

The electric field is defined as a vector field that associates to each point in space the electrostatic (Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point

First, in this sentence, i'm doubtful about 'electrostatic force'. As i know, moving charges also make electric field.

This implies there are two kinds of electric fields: electrostatic fields and fields arising from time-varying magnetic fields.

And i think, in here, there is electric field which is not belonging to 'electrostatic field and field time-varying magnetic fields'. For example, steady current, not in wire, makes electric field but don't make time varying magnetic field..

Is there something I'm thinking wrong? I think above sentences are uncomplete

• There is only one electromagnetic field in the universe. But, since electromagnetism is linear, it means we can add electric fields contributions to others. Hence the apparent multiple electric and magnetic fields. Nov 5, 2023 at 11:23
• I believe the goal of these sentences is to highlight the distinction between the curl-free field that allows for easier description when we don't have any time-varying magnetic fields, and the full electromagnetic treatment required with time varying magnetic fields. Traditionally these fields are called electrostatic and electrodynamic. The former doesn't mean the entire system is static, but rather that a static description of the corresponding charge distribution suffices for me to calculate the electric field. Nov 5, 2023 at 11:27
• @KarimAED, Thank you, but there is something i want to check. First, Do you mean this mean actually conservative and non-conservative? And second, do you agree this sentence 'Two kinds of electric fields: electrostatic( this static mean entire system is static) fields and electrodynamics field' ?
– KHJ
Nov 5, 2023 at 11:38
• Yes, without time-varying magnetic fields the electric field is conservative, if time varying magnetic fields exist, it is not. In general, there is no such distinction between static and dynamic fields in nature of course. However, historically we first discovered laws that governed static situations, and later ones that governed dynamic situations. In that sense one can make a distinctions between fields for which static description suffices, and ones which require a full electrodynamic treatment. I believe the article is consistent in itself, and is a reasonably basic intro to the subject. Nov 5, 2023 at 11:53
• @KarimAED, Thank you for kindly answer
– KHJ
Nov 5, 2023 at 12:03

Ignore the word "static" in the first quote, or at least don't interpret it to mean "this only holds in the static case" in which all charges are stationary. The units of the electric field are Newtons per Coulomb, so the field at each point is a measure of the force imparted per unit charge at that point. This is still correct even when charges are moving and hence the electric/magnetic fields may be time dependent.

The second sentence is worded a little confusingly, we don't typically distinguish the electric field arising from electrically charged particles:

$$\nabla\cdot \vec E=\frac{\rho}{\epsilon_0} \tag{1}$$

and those arising from time dependent magnetic fields

$$\nabla\times \vec E=-\frac{\partial \vec B}{\partial t} \tag{ii}$$

in situations in which both exist. We just have one electric field which separately satisfies all of Maxwell's equations. So you are right in both cases, the wording is just a little imprecise in the Wikipedia article.