In general, same-sign charged particles repel one another, while different-sign charged particles attract. This is expressed quantitatively in Coulomb's law, which states that the magnitude of the electrostatic repelling force between two particles is proportional to the product of their charges and the inverse square of the distance between them.
The electric charge of a macroscopic object is the sum of the electric charges of its constituent particles. Often, the net electric charge is zero, because it is favorable for the number of electrons in every atom to equal the number of protons (or, more generally, for the number of anions, or negatively charged atoms, in every molecule to equal the number of cations, or positively charged atoms). When the net electric charge is non-zero and motionless, one has the phenomenon known as static electricity. Even when the net charge is zero, it can be distributed non-uniformly (e.g., due to an external electric field, or due to molecular motion), in which case the material is said to be polarized. The charge due to the polarization is known as bound charge, while the excess charge brought from outside is called free charge. The motion of charged particles (e.g., of electrons in metals) in a particular direction is known as electric current.
Formally, a measure of charge should be a multiple of the elementary charge e (charge is quantized), but since it is an average, macroscopic quantity, many orders of magnitude larger than a single elementary charge, it can effectively take on any real value. Furthermore, in some contexts it is meaningful to speak of fractions of a charge; e.g. in the charging of a capacitor.
As reported by the Ancient Greek philosopher Thales of Miletus around 600 BC, charge (or electricity) could be accumulated by rubbing fur on various substances, such as amber. The Greeks noted that the charged amber buttons could attract light objects such as hair. They also noted that if they rubbed the amber for long enough, they could even get a spark to jump. This property derives from the triboelectric effect.
In 1600 the English scientist William Gilbert returned to the subject in De Magnete, and coined the New Latin word electricus from ηλεκτρον (elektron), the Greek word for "amber", which soon gave rise to the English words "electric" and "electricity." He was followed in 1660 by Otto von Guericke, who invented what was probably the first electrostatic generator. Other European pioneers were Robert Boyle, who in 1675 stated that electric attraction and repulsion can act across a vacuum; Stephen Gray, who in 1729 classified materials as conductors and insulators; and C. F. du Fay, who proposed in 1733 that electricity came in two varieties which cancelled each other, and expressed this in terms of a two-fluid theory. When glass was rubbed with silk, du Fay said that the glass was charged with vitreous electricity, and when amber was rubbed with fur, the amber was said to be charged with resinous electricity. In 1839 Michael Faraday showed that the apparent division between static electricity, current electricity and bioelectricity was incorrect, and all were a consequence of the behavior of a single kind of electricity appearing in opposite polarities. It is arbitrary which polarity you call positive and which you call negative. Positive charge can be defined as the charge left on a glass rod after being rubbed with silk.
One of the foremost experts on electricity in the 18th century was Benjamin Franklin, who argued in favour of a one-fluid theory of electricity. Franklin imagined electricity as being a type of invisible fluid present in all matter; for example he believed that it was the glass in a Leyden jar that held the accumulated charge. He posited that rubbing insulating surfaces together caused this fluid to change location, and that a flow of this fluid constitutes an electric current. He also posited that when matter contained too little of the fluid it was "negatively" charged, and when it had an excess it was "positively" charged. Arbitrarily (or for a reason that was not recorded) he identified the term "positive" with vitreous electricity and "negative" with resinous electricity. William Watson arrived at the same explanation at about the same time.
Electrification by friction
Let a piece of glass and a piece of resin, neither of which exhibits any electrical properties, be rubbed together and left with the rubbed surfaces in contact. They will still exhibit no electrical properties. Let them be separated. They will now attract each other.
If a second piece of glass be rubbed with a second piece of resin, and if the piece be then separated and suspended in the neighbourhood of the former pieces of glass and resin, it may be observed:
1) that the two pieces of glass repel each other.
2) that each piece of glass attracts each piece of resin.
3) that the two pieces of resin repel each other.
These phenomena of attraction and repulsion are called Electrical phenomena and the bodies which exhibit them are said to be 'electrified', or to be 'charged with electricity'.
Bodies may be electrified in many other ways, as well as by friction.
The electrical properties of the two pieces of glass are similar to each other but opposite to those of the two pieces of resin: the glass attracts what the resin repels and repels what the resin attracts.
If a body electrified in any manner whatever behaves as the glass does, that is, if it repels the glass and attracts the resin, the body is said to be 'vitreously' electrified, and if it attracts the glass and repels the resin it is said to be 'resinously' electrified. All electrified bodies are found to be either vitreously or resinously electrified.
It is the established practice of men of science to call the vitreous electrification positive, and the resinous electrification negative. The exactly opposite properties of the two kinds of electrification justify us in indicating them by opposite signs, but the application of the positive sign to one rather than to the other kind must be considered as a matter of arbitrary convention, just as it is a matte of convention in mathematical diagram to reckon positive distances towards the right hand.
No force, either of attraction or of repulsion, can be observed between an electrified body and a body not electrified.
We now know that the Franklin/Watson model was fundamentally correct. There is only one kind of electrical charge, and only one variable is required to keep track of the amount of charge. On the other hand, just knowing the charge is not a complete description of the situation. Matter is composed of several kinds of electrically charged particles, and these particles have many properties, not just charge.
The most common charge carriers are the positively charged proton and the negatively charged electron. The movement of any of these charged particles constitutes an electric current. In many situations, it suffices to speak of the conventional current without regard to whether it is carried by positive charges moving in the direction of the conventional current and/or by negative charges moving in the opposite direction. This macroscopic viewpoint is an approximation that simplifies electromagnetic concepts and calculations.
At the opposite extreme, if one looks at the microscopic situation, one sees there are many ways of carrying an electric current, including: a flow of electrons; a flow of electron "holes" which act like positive particles; and both negative and positive particles (ions or other charged particles) flowing in opposite directions in an electrolytic solution or a plasma).
Beware that in the common and important case of metallic wires, the direction of the conventional current is opposite to the drift velocity of the actual charge carriers, i.e. the electrons. This is a source of confusion for beginners.
Aside from the properties described in articles about electromagnetism, charge is a relativistic invariant. This means that any particle that has charge Q, no matter how fast it goes, always has charge Q. This property has been experimentally verified by showing that the charge of one helium nucleus (two protons and two neutrons bound together in a nucleus and moving around at high speeds) is the same as two deuterium nuclei (one proton and one neutron bound together, but moving much more slowly than they would if they were in a helium nucleus).
The total electric charge of an isolated system remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function. The conservation of charge results in the charge-current continuity equation. More generally, the net change in charge density within a volume of integration is equal to the area integral over the current density on the surface of the area , which is in turn equal to the net current :
Thus, the conservation of electric charge, as expressed by the continuity equation, gives the result:
The charge transferred between time and is obtained by integrating both sides:
where I is the net outward current through a closed surface and Q is the electric charge contained within the volume defined by the surface.