electrons - What is charge?

I know this isn't the right place for asking this question, but in other places the answers are so awfull.. I'm studying eletricity, so, I start seeing things like "charges", "electrons has negative charges",etc. But I didn't quite understand what charge is. I search a little bit on the internet and found it related to electromagnetic fields, then I thought "negative and positive may be associeted with the behaviour of the particle in the field, great!", but the articles about e.m. fields already presuppose "negative" and "positive" charges. In other places, I see answers relating charges to the amount of electrons/protons in an atom, but if that's right, the "negative" electron is an atom without any protons? What about the neutron? So, my questions are (1) What are charges; and (2) How a particle can "be" electrically charged. What does that really mean? Thanks for your time.

Answer

I would say that charge is a theoretical prescription describing a way of how a particle interacts with electromagnetic field. Since we are talking about a theory that should describe and predict various phenomena, we need to start with definition of fundamental object.

If we are talking about Newtonian mechanics we face phenomena related to interactions of particles with each other by a direct mechanical contact. We characterize these interactions by force, momentum, etc. Fundamental characteristics of a body will be the mass. Theoretically, you may consider objects of positive, negative or zero mass in mechanics. However, from experiment we know, that there are no objects with negative mass.

The same is true for electrodynamics, where we see objects interacting through a field. Now to describe the ability of an object to generate or to fill this field, we introduce the charge. So, as was already said by zeal charge is just a property of an object, same as mass.

Concerning your second question. Firstly, one should note that any object may have any charge irrespective of electrons. However, we know that atom is a complex object composed from electrons, protons and neutrons. Hence, in order to figure out charge of an atom we should assign some charges to its fundamental constituents.

From experiments we know that electrons, neutrons and protons interact with each other and with electromagnetic field in such a way, that we may define $q_e=-1$, $q_p=+1$, $q_n=0$. Now, just by summing charges of constituents of a complex object we can derive its charge.

Hence, in brief: charge is such theoretical prescription in electrodynamics, that allows to predict electromagnetic phenomena.