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Introduction
Consider this outline as an approach to defining ‘electric charge’:


 * At one level of explanation of matter, matter consists of atoms.
 * Electric charge is a property of matter manifesting in certain of the particle constituents of the atoms of matter.
 * Studying atoms at the first level of their substructure, viz., the nucleus and surrounding electrons, can provide a fruitful starting point for explaining electric charge.


 * As a starting point, note that:
 * Electrons can maintain their location surrounding and revolving about the nucleus only because a radial force of attraction on them exists directed toward the nucleus. Otherwise the electrons would fly off.


 * Experiments reveal that:
 * The force of attraction between the nucleus and electrons greatly exceeds the gravitational force generated by the masses of the two groups of particles;
 * Therefore a force differing from the force of gravitation is operating, requiring a new designation;
 * For historical reasons discussed later, we designate the force an ‘electric force’.
 * Experiments reveal also that:
 * The force of attraction occurs between the protons in the nucleus and the surrounding electrons, the two groups normally equal in number;
 * The magnitude of the electric force varies inversely with the square of the distance of separation over which the force operates.


 * Experiments reveal also that:
 * The electric force between two spatially separate protons is one of repulsion rather than of attraction;
 * The electric force between two spatially separate electrons likewise is one of repulsion rather than of attraction;
 * When separated by the same distance, the magnitude of the electric force is the same between a proton and an electron, a proton and a proton, and an electron and an electron.


 * Those experiments permit the conclusions that:
 * The electric force can be one either of attraction or repulsion;
 * Given that protons and electrons differ in mass by several orders of magnitude, the electric force does not depend on the masses of the interacting particles;
 * Therefore some quantitative property other than mass must generate and respond to the electric force between interacting particles;
 * call that property ‘electric charge’, and symbolize its unit of magnitude, q.
 * The ‘quality’ of the proton’s electric charge must differ from the ‘quality’ of the electron’s electric charge, otherwise protons and electrons could not generate and respond to either an attractive or repellent electric force depending on which interacts with which;
 * call the quality of the proton’s electric charge ‘positive’ and that of the electron’s ‘negative’, in keeping with historical designations arbitrarily assigned during the history of studies of electric phenomena on the macroscopic scale.
 * From the above discussion, we can formulate a provisional working definition of electric charge as follows:
 * Atoms of the chemical elements heavier than hydrogen...

Continue in this vein....

Tentative lede to student level treatment
Electric charge refers to a fundamental property of matter upon which rests the numerous phenomena in the sciences and engineering of electricity and electromagnetism.

Electric charge manifests itself, in one guise, as a property of the two earliest discovered constituents of the historically conceived homogeneous and indivisible atom, the subatomic particles, electrons and protons, a property that endows an electron and a proton, though spatially separate, with the ability to attract each other with a force of attraction, called the electric force. The electric force of attraction between the two particles differs from their gravitational force of attraction in that the magnitude of the electric force, for a given distance of separation of the two particles, is orders of magnitude greater than the force of gravitational attraction between them associated with their masses, greater by ~1042 fold. For that reason, the force of attraction between an electron and a proton does not depend on the masses of the two particles, whose gravitational force can be ignored as a contributor to the magnitude of the attractive force.

A non-gravitationally-mediated force also exists between two spatially separate electrons, and between two spatially separate protons, but unlike the force of attraction between an electron and a proton, the force between two electrons is one of repulsion, as is the force between two protons. Thus the common expression, “like charges repel, unlike charges attract”.

Scientists had established much of the above by the early 20th century, as evidenced from the discussion in first few chapters of the 1907 still instructively readable classic, The Corpuscular Theory of Matter, by the discoverer of the electron, Joseph John Thomson (1856-1940) '''

Older version to be revised
In reference to the physics and chemistry of electricity, charge, or more specifically, electric charge, is a fundamental property of matter that causes matter having that property to generate and react to a force of attraction or repulsion to spatially separate matter that likewise manifests the property of electric charge.

Whatever constitutes electric charge constitutes it as two separate qualities, or polarities, assigned the names 'positive' and 'negative', or 'plus' and 'minus'. The attractive force between electrically charged entities arises between oppositely-charged entities&mdash;positive-negative&mdash;whereas the repulsive force arises between like-charged entities&mdash;positive-positive, or negative-negative.

Familiar examples of positively charged matter are protons, constituents of the nuclei of atoms, and familiar examples of negatively charged matter are electrons, constituents of atoms that surround their nuclei.

Given that the terms 'positive' and 'negative' serve only as labels to distinguish the two polarities observed in the electric charge of matter, 'positivity' and 'negativity' do not themselves imply anything about the fundamental nature of electric charge. Other labels connoting bi-polarity, such as yin/yang, black/white, or bitter/sweet, could serve for labeling.

The atoms that comprise the chemical elements of the periodic table, while consisting in part of the electrically charged particles, protons and electrons, do not themselves manifest an electric charge, because protons in the nuclei and the surrounding electrons are equal in number and quantity of charge, that balance ensuring that the atoms as a whole manifest no net electric charge&mdash;a state referred to as electrical neutrality.

Discovery and naming of electric charge
The ancient Greeks as far back as the beginning of the 6th century BCE, beginning with Thales of Miletus, had observed some of the simple phenomenology related to electric charge, Thales demonstrating it using the fossilized tree resin, amber, rubbed with cloth:

In 600 B.C. Thales, erudite philosopher and astronomer in the thriving Ionian port of Miletus, observed the special qualities of the rare yellow orange amber, jewel-like in its hardness and transparency. If rubbed briskly with a cloth, Thales showed, amber seemed to come alive, causing light objects—like feathers, straw, or leaves—to fly toward it, cling, and then gently detach and float away. Amber was similar to a magnet in its qualities, yet it was not a lodestone. As a youth, Thales of Miletus had studied in the sacred Egyptian cities of Memphis and Thebes. Perhaps it was there, under the burning sun, that this earliest of Greek philosophers first learned from the priests about the prized amber, with its seeming possession of a soul.

Thales, it appears, believed amber an animate thing, something with soul.

The Greek word for amber, elektron, ultimately through Latin, electrum, gave rise to the English words, electrical and electric &mdash; words used to refer to the amber phenomenon before the publication of William Gilbert's landmark work, De magnete, in 1600, describing the results of the first systematic experimental studies of magnetic and electrical phenomena in Western science.

The word, charge, used in its electrical sense, was first used by Benjamin Franklin, in 1747, as a verb, and subsequently by him as adjective and noun: Our spheres are fixed on iron axes, which is passed through them. At one and of the axis there is a small handle, with which you turn the sphere like a common grindstone. This we find very commodious, as the machine takes up little room, is portable, and may be enclosed in a tight box, when not in use. 'Tis true, the sphere does not turn so swift as when the great wheel is used, but swiftness we think of little importance, since a few turns will charge the phial, etc., sufficiently. [italics added]

Presumably, Franklin, who, in his many writings, frequently used the word, charge, and its variant forms (charging, charged, etc.), in its non-electrical sense, had in mind the word's sense of 'loading' or 'filling' something:

charge - ORIGIN: Middle English (in the general senses ‘to load’ and ‘a load’): from Old French charger (verb), charge (noun), from late Latin carricare, carcare ‘to load,’ from Latin carrus ‘wheeled vehicle.’...Examples: load or fill (a container, gun, etc.) to the full or proper extent: will you see to it that your glasses are charged? | fill or pervade (something) with a quality or emotion: the air was charged with menace.

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synbio
Somewhat more broadly, the American Chemical Society’s journal, ACS Synthetic Biology, states:

It lists the following topics as appropriate for a journal on synthetic biology:

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