# Meaning of negative density

Charge density depends on the area/volume and the amount of charge. Before electromagnetism I used to think of density as being positive only.
What is the intuitive meaning of negative density? Does it just tells us that the charge is negative or is there more information related to the negative sign?

• think of a gas of electrons. How would you define the charge density? Now take neutral matter, which is made of charged particles like electrons and protons? How come that charge density is zero for neutral matter when it actually contains charge distributions? – Phoenix87 May 8 '15 at 17:20
• I didn't know it was neutral :P I thought of density as mass density until now, so the amount of stuff per amount of space. Could you answer your own questions please? Now I'm curious – Yuri Borges May 8 '15 at 17:34
• The idea is that you define charge density whenever you have some charges (like mass density whenever you have some mass spread across a certain region). If you separate positive and negative charges and you just count them you end up with two positive densities whose sum is a positive quantity. So for neutral matter, where there are in general both positive and negative charges cancelling each other, you would have a positive charge density, unless you subtract one density from the other, which means that you can assume one of the two to be negative in the first place. – Phoenix87 May 8 '15 at 17:37

If the electric charge density of a region of space is negative, that would mean that there are more negative charges than positive charges in that region.

When people use the word "density" casually, they usually mean mass density (or sometimes number density). Mass (as far as we know) can only be positive, and the number of particles can only be positive, thus those types of densities are only positive.

Electric charge, however, is free to take positive or negative values, because of the nature of electric charge - some particles have positive charges (e.g. protons), and some have negative charge (e.g. electrons).

It tells us that the charge is negative.
Surface charge density is negative when the surface is covered by -ve charge. Same goes for volume charge density.

Like any density, charge density can depend on position, but charge and thus charge density can be negative.

Wikipedia

• Woah, that was close. I was just ahead by 6s :) – user80772 May 8 '15 at 17:23

The term negative charge density is incorrect. By definition: charge density is the amount of charge per unit length (linear charge density), unit area (surface charge density) or unit volume (volume charge density). Corresponding units are: $$C/m$$, $$C/m^2$$ and $$C/m^3$$ respectively. There can not be less than zero charge, therefore charge density can not be negative. Consequently, there can be a density of negative charge but can not be negative charge density.
The concept of charge density should not be mixed with existence of negative and positive charges and related net charge concept. Example: hydrogen atom has one negative charge (-1e) and one positive charge (+1e), so in total the net charge of the system is 0. Charge density plotted along the line drawn through the atom center will have two spikes, in the center and one radius apart. Everywhere else the charge density would be zero, since there is no charge. For both spikes the density would be the same, since there only one charge per unit length, and positive, regardless of the fact that in the center the charge is positive and one radius apart it is negative.