Electric charge

See also: Electricity

Introduction

In reference to the physics and chemistry of electricity, 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 charge. Classically, two types of charge are known, magnetic and electric. The distinguishing property of electric charge is that electric charges can be isolated, while while an isolated magnetic charge or magnetic monopole never has been observed. Electric charges interact with magnetic charges only when in relative motion one to the other.

Once you have established those basic ideas about electricity, "like charges repel and unlike charges attract", then you have the foundation for electricity and can build from there. —Electric Charge, Hyperphysics Online

Whatever constitutes electric charge, it exists with 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—positive-negative—whereas the repulsive force arises between like-charged entities—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—a state referred to as electrical neutrality.

Classically, electric charge occurs in discrete quantities, multiples of the charge of the electron. At the level of the elementary particle, quarks have fractional charges, multiples of 1/3 of an electron charge.

Electric charge is conserved, that is the total amount of electric charge does not change, although it can be partitioned differently among electrically charged objects.

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:

That little piece of amber rubbed by Thales, some 2,500 years ago, appeared then to be very insignificant. Had the world but known, it was fraught with vast possibilities; for, in point of fact, Thales had unconsciously rediscovered Aladdin's Wonderful Lamp. As he rubbed, the Genie of electricity appeared, and demanded, "What wouldst thou have? I am ready to obey thee as the slave of the lamp, I and the other slaves of the lamp." But the question remained unanswered. Neither Thales nor the witnesses of his experiment made any request nor asked its genii to aid them. They had ears, but they heard not, and so the genie disappeared, with all that he was both willing and able to do left undone. —E.J. Houston, 1905

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 — 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.

William Gilbert, founder of electrical science

“Although the precise beginnings of electrical science are contestable, no one doubts that William Gilbert (1540–1603), an Englishman, carried out the first sustained and influential research on electrical phenomena.”

Relation to forces

Note: The SI units are used below.

The force upon a stationary electrically charged point body with charge q₁ due to another such body with charge q₂ is governed by Coulomb's law:

$\mathbf {F_{12}} =-{\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{1}q_{2}}{r_{12}^{2}}}\mathbf {{\hat {u}}_{12}} \ ,$

where r₁₂ is their separation and û₁₂ is a unit vector pointing from charge one to charge two. The minus sign indicates that the force F is repulsive when both charges have the same sign. The quantity ε₀ is the electric constant, also called the permittivity of free space, and it is assumed that both charges are in classical vacuum.

For distributions of charge, rather than point charges, the force at any position in space can be found using Poisson's equation:

$\nabla ^{2}\varphi =-{\frac {\rho (\mathbf {r} )}{\varepsilon _{0}}}\ ,$

one of the Maxwell equations. Quantity ∇² is the Laplacian operator of vector calculus. Here ρ(r) is the charge density per unit volume located at position r, and φ(r) is the electric potential at position r. This equation is deceptively simple in appearance, and its solution involves careful consideration of the the materials in the space and their geometries. Having found the potential by solving this equation, the force upon a test charge of magnitude q (a point charge considered too small to affect the force in itself) at position r is determined by:

$\mathbf {F} (\mathbf {r} )=-q\nabla \varphi \ ,$

where ∇ is the gradient operator of vector calculus. The quantity

$\mathbf {E} (\mathbf {r} )=-\nabla \varphi (\mathbf {r} )\ ,$

is called the electric field at point r.

When charges are moving relative to each other, the forces between them are much more complex. Moving charges constitute an electric current, generating magnetic fields and magnetic forces. See the article Liénard–Wiechert potentials.