= Electric charge
{wiki}
<Electric charge> is an additive, signed property of matter that determines its coupling to the <electromagnetic field>. Write a particle's <electric charge> as $q$, or a collection's total <electric charge> as $Q$; the <SI> unit is the <coulomb>, $\mathrm C$. A stationary test particle in an <electric field> experiences <electric force> $\mathbf F=q\mathbf E$, while motion adds the magnetic part of the <Lorentz force>. <Electric charge> both produces an <electric field> and determines the response to one. For two stationary point particles in <vacuum>, <Coulomb's law> makes like signs repel and opposite signs attract. The choice of which sign to call positive is a convention, used consistently: <protons> carry $+e$ and <electrons> carry $-e$, where $e$ is the <elementary charge>. https://www.feynmanlectures.caltech.edu/II_01.html[Feynman, Leighton and Sands, II.1: electrical forces, fields and the Lorentz force]{ref}.
Additivity means adding signed <electric charges>, rather than their magnitudes:
$$
Q=\sum_i q_i,\qquad Q=e(N_p-N_e)
$$
for ordinary matter containing $N_p$ <protons>, $N_e$ <electrons>, and electrically neutral <neutrons>. A toy collection with seven <protons> and ten <electrons> has $Q=-3e$, however much neutral material accompanies it. <Charge neutrality> means $Q=0$; it does not mean an absence of charged constituents. Nor does it guarantee an absence of <electric force>: the spatial arrangement of positive and negative <electric charges> matters, as illustrated by an <electric dipole>. This makes a tiny imbalance in an otherwise nearly neutral object physically important. https://www.feynmanlectures.caltech.edu/II_01.html#Ch1-S1[Feynman, Leighton and Sands, II.1.1: neutrality, imbalance and residual electrical forces]{ref}.
<Charge conservation> states that a collection closed to transport of <electric charge> keeps its total signed $Q$. If $n$ <electrons> move from object A to object B without other exchange, then $\Delta Q_A=+ne$ and $\Delta Q_B=-ne$; the sum is unchanged. The amount of positive <electric charge> alone need not be conserved: creation of an <electron> and a <Positron> adds opposite <electric charges> with zero sum. These bookkeeping rules let us distinguish separation or transport of <electric charge> from creation of net <electric charge>. https://www.feynmanlectures.caltech.edu/I_04.html#Ch4-S4[Feynman, Leighton and Sands, I.4.4: conservation of net charge]{ref}.
A simple motivating experiment uses two charge-producing paddles, a conducting pail on an insulating support, a grounded outer shield and a high-input-impedance <electrometer>. Zero the pail, then isolate it. Rub the initially neutral paddles together, keeping their charged surfaces away from other objects. Lower each deeply into the pail without touching: the <electrometer> gives opposite signs. Inserting both together tests cancellation. For a separate contact test, insert one charged paddle without touching and withdraw it: the reading returns to zero. Repeat after zeroing, this time touching the inner wall before withdrawal: a residual reading shows transfer of <electric charge>. Zero the pail and reinsert the paddle to test how much <electric charge> remains on it. PASCO describes these procedures in https://cdn.pasco.com/product_document/Basic-Electrostatics-Sys-Manual-ES-9080B1.pdf#page=13[Basic Electrostatics System manual, demonstrations 1A and 1B, printed pp. 13–16].
\Image[/electric-charge-transfer-schematic.png]
{title=<Electric charge> redistribution versus transfer in a conducting pail}
{description=Original qualitative schematic for a positively charged inserted object. Without contact, <electrostatic induction> separates negative inner-surface and positive outer-surface <electric charges>, while the pail's total remains zero. Contact can leave net positive <electric charge> after withdrawal. Symbols are not particle counts; no measured readings are plotted.}
{source=electric-charge-transfer-schematic.py}
The crucial control is withdrawal without contact: a response during insertion can come from <electrostatic induction>, which redistributes the pail's existing <electric charge>. In the fixed-geometry approximation, the <electrometer> measures <electric potential difference> proportional to enclosed <electric charge>, with conversion set by effective <capacitance>; a voltage reading is not already a measurement in <coulombs>. Opposite readings and their cancellation test additivity and <charge conservation> within resolution. Leakage or accidental contact spoils that interpretation, and contact need not transfer all the paddle's <electric charge>. This macroscopic experiment cannot resolve <elementary charge> steps: that requires the much smaller particles of the <oil drop experiment>.
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