Electric Charge & Its Properties

Pull a wool sweater over your head in a dry winter room and the crackle you hear is a property of matter announcing itself — one that is stronger than gravity by almost forty orders of magnitude, comes in exactly two varieties, can never be created or destroyed, and is delivered only in whole-number multiples of a single indivisible coin. That property is electric charge, and this entire track — fields, potential, circuits, magnetism, electromagnetic waves — is the story of what charge does. Here is what makes charge worth a whole module before a single force formula appears: everything you will compute later depends on four bookkeeping rules that charge obeys without exception. Charge comes in two kinds that cancel; it adds like a signed number; the total in an isolated system is fixed forever; and it is quantised in steps of $e = 1.6\times10^{-19}\ \mathrm{C}$ . Examiners across every board — CBSE and ICSE one-markers, NEET's "which charge is impossible?" staple, JEE's charge-counting warm-ups, AP and IB conceptual items — test these four rules directly, because a student who is fuzzy on them mis-signs every later calculation. Twenty minutes here buys you the currency of electromagnetism. By the end you will know what a coulomb actually is (an absurdly large unit, and why), how to count electrons behind any charge, and why "neutral" is one of the most misleading words in physics.

Key takeaways

Charge is an intrinsic property of matter, like mass — but it comes in two kinds, positive (protons) and negative (electrons), and unlike gravity the resulting forces can cancel.
Charge is a scalar with a sign: net charge is the plain algebraic sum $q_{\text{net}} = q_1 + q_2 + \cdots$ (additivity).
Charge is conserved: the total charge of an isolated system never changes — charging anything only ever moves electrons from one place to another.
Charge is quantised: $q = ne$ with $n$ an integer and $e = 1.6\times10^{-19}\ \mathrm{C}$ ; a charge of $2.5e$ on a free object is impossible, and examiners test exactly this.
One coulomb is enormous — about $6.25\times10^{18}$ electrons; real static charges are microcoulombs and nanocoulombs.
Key idea: charge is a conserved, quantised, signed quantity — every electrostatics calculation you will ever do is bookkeeping built on those three words.

The core insight

Electric charge is a signed scalar property of matter that adds algebraically, is conserved absolutely in every isolated system, and exists only in integer multiples of the elementary charge $e = 1.6\times10^{-19}\ \mathrm{C}$ .

Where this lives today

The 2019 redefinition of the SI quietly crowned this module's small print: the coulomb is now defined by fixing $e$ , so "one coulomb" literally means " $6.241\,509\ldots\times10^{18}$ elementary charges." Metrology labs close the loop with single-electron pumps — nanoscale devices that shuttle electrons one at a time at radio frequencies, building a current you can count. Quantisation, once Millikan's delicate inference, is now an engineering resource. Conservation, meanwhile, is the sharpest scalpel in particle physics. Every reaction recorded at the LHC is audited for charge balance before anything else; a single verified event with unbalanced charge would demolish the Standard Model overnight. None has ever been seen. And the "impossible" fractional charges of quarks ( $\pm e/3$ , $\pm 2e/3$ ) show up only in bound combinations that restore integer totals — nature enforcing equation (3) at the door, even while breaking it in the basement.

The physical picture

Matter is built from atoms, and atoms are built from charged parts: a tiny nucleus holding positive protons (with neutral neutrons), surrounded by negative electrons. The proton and the electron carry exactly equal and opposite charges — measured to better than one part in $10^{21}$ — so an atom with equal numbers of each is neutral. That word deserves suspicion from day one. A "neutral" body is not empty of charge; it is a warehouse of colossal, perfectly balanced charge. Your own body contains roughly $10^{28}$ electrons and an equal positive charge sitting in nuclei. Neutrality is a cancellation, not an absence. Charging an object means disturbing that balance — and in solids there is only one way to do it: move electrons. Protons are locked deep inside nuclei, which are themselves locked into the material; the outermost electrons are the only movable currency. Rub a glass rod with silk and a few electrons ( $\sim 10^{12}$ of them — about one atom in a million-billion of the body's total) hop from glass to silk. The glass, having lost electrons, is left positive; the silk, having gained them, goes equally negative. Nothing was created. The ledger balances to the last electron.

Figure

Charging is electron bookkeeping — the ledger always balances

Two immediate consequences of this picture run the whole subject. First, the body that loses electrons ends up positive — students reflexively attach "gains something" to "+", and examiners punish it. Second, because charging is electron transfer, a charged body's mass changes, microscopically: a negatively charged balloon is heavier than it was, a positively charged rod lighter, by the mass of the transferred electrons. It is a favourite one-marker. Why does everyday matter feel electrically silent when it is stuffed with charge? Because the two kinds cancel with fanatical precision, and — as you will compute in Coulomb's Law — the electric force is so strong that nature cannot tolerate visible imbalances. The static crackle of a sweater is an imbalance of about one electron per $10^{16}$ ; that whisper of imbalance is already enough to make sparks jump.

The four properties, precisely

Two kinds. Charge du Fay called "vitreous" and "resinous" and Franklin renamed positive and negative: like kinds repel, unlike kinds attract. The names are pure convention — Franklin guessed which fluid "flowed," and his coin-toss left the electron labelled negative, a historical accident electronics students curse to this day. What matters physically is that the two kinds cancel: this is what makes electricity different from gravity, where mass has one sign and every contribution only ever adds.

Additivity. Charge is a scalar with a sign, and the total charge of a system is the plain algebraic sum of its parts:

q_{\text{net}} = q_1 + q_2 + q_3 + \cdots \qquad (1)

where: each $q_i$ enters with its sign. A system holding $+5\ \mu\mathrm{C}$ , $-8\ \mu\mathrm{C}$ and $+3\ \mu\mathrm{C}$ has net charge $0$ — even though it contains $16\ \mu\mathrm{C}$ of "gross" charge that can still exert and feel forces. Contrast mass, which is also additive but never negative: a box of matter can never have zero mass, but it can easily have zero net charge. No direction is attached — charge is a scalar, not a vector, however much the $+$ and $-$ signs tempt you to think otherwise.

Conservation. The deepest of the four:

q_{\text{total}}^{\text{isolated system}} = \text{constant, for all time} \qquad (2)

where: isolated means no charge crosses the system's boundary. Charge can move (rubbing), redistribute (sharing between conductors), even appear in new particles — but only in balanced pairs. When a high-energy photon (charge $0$ ) converts into matter, it must produce an electron ( $-e$ ) and a positron ( $+e$ ) together: $0 = -e + e$ , the ledger enforced even in particle creation. No experiment in history has ever seen net charge appear or vanish. When a problem says a body "loses its charge to the air," the charge has leaked into the air's ions — conservation holds; only the system boundary changed.

Quantisation. Charge is not a continuous fluid. Every free object's charge is an integer number of elementary charges:

q = ne, \qquad n = 0, \pm 1, \pm 2, \ldots, \qquad e = 1.6\times10^{-19}\ \mathrm{C} \qquad (3)

where: $e$ — the magnitude of the charge on one proton (or one electron, with a minus sign); $n$ — positive for electron deficit, negative for electron excess. Since 2019, $e$ is fixed exactly (at $1.602\,176\,634\times10^{-19}$ C) as a defining constant of the SI; use $1.6\times10^{-19}$ C in every board and entrance calculation. Equation (3) is a divisibility test: a reported charge of $4.0\times10^{-19}\ \mathrm{C}$ is legal ( $n = 2.5$ ? No — check: $4.0/1.6 = 2.5$ , illegal!), while $4.8\times10^{-19}\ \mathrm{C}$ is fine ( $n = 3$ ). One caution for the curious: protons and neutrons are built of quarks carrying $\pm e/3$ and $\pm 2e/3$ , but quarks never appear alone — every particle you can isolate obeys equation (3) as written.

Figure

The quantisation ladder — allowed and forbidden charges

The unit itself deserves a number. One coulomb (the SI unit, defined via the ampere: $1\ \mathrm{C} = 1$ ampere-second) corresponds to

N = \frac{1\ \mathrm{C}}{1.6\times10^{-19}\ \mathrm{C}} = 6.25\times10^{18}\ \text{elementary charges} \qquad (4)

where: $N$ — the electron count behind one coulomb. That is why the coulomb is a giant's unit: rubbing produces nanocoulombs to microcoulombs, a lightning stroke transfers a few tens of coulombs, and two whole coulombs sitting a metre apart would repel with about $9\times10^9$ N — the weight of a million tonnes (that number is the opening act of the next-but-one module, Coulomb's Law). Everyday electrostatics lives in $\mu$ C ( $10^{-6}$ C) and nC ( $10^{-9}$ C); convert to coulombs before computing, always.

property	statement	exam reflex
two kinds	like repel, unlike attract	signs do the direction bookkeeping
additivity	$q_{\text{net}} = \sum q_i$ , signs included	scalar sum — never add magnitudes blindly
conservation	isolated total fixed forever	track where electrons went, body by body
quantisation	$q = ne$ , $e = 1.6\times10^{-19}$ C	divide any charge by $e$ : integer or impossible

Derivation AWhy rubbing can only transfer electrons — and what that does to each body

We want to justify the rule every charging problem silently uses: in solids, only electrons move, so the rubbed pair ends up with exactly equal and opposite charges, and each body's mass shifts by the mass of the transferred electrons. The strategy is to argue from atomic structure — where each kind of charge lives and what holds it there — and then run the conservation ledger for the glass–silk pair. Watch for the payoff at the end: the ledger forces the two final charges to be equal in magnitude, which is not an extra assumption but a consequence.

Step 1. Locate the charges. Protons sit inside nuclei, bound by the nuclear force with energies around a million times larger than chemical energies; the nuclei themselves are locked into the solid's structure. The outermost atomic electrons are held only by chemical-scale energies. Why this matters: rubbing supplies chemical-scale energy — enough to pry loose an outer electron, hopelessly too little to extract a proton. So the only mobile charge in a solid is the electron.

Step 2. Let friction transfer $n$ electrons from glass to silk (glass binds its surface electrons more weakly). The glass's charge changes by $0 - (-ne) = +ne$ ; the silk's by $-ne$ .

Step 3. Apply conservation to the isolated pair: total before $= 0$ , so total after $= (+ne) + (-ne) = 0$ . ✓ The magnitudes must match: whatever one body loses, the other gains, electron for electron. "The glass got $+2\ \mu$ C and the silk $-3\ \mu$ C" is impossible physics, not a rounding error. Why examiners care: many trap options break exactly this symmetry, betting you won't audit the total.

Step 4. Read off the mass ledger. The silk gained $n$ electrons, so its mass rose by $\Delta m = n m_e$ with $m_e = 9.1\times10^{-31}$ kg; the glass lost the same. For a typical $n \sim 10^{12}$ , $\Delta m \sim 10^{-18}$ kg — utterly unmeasurable on a balance, but the sign of the change ("negatively charged body is heavier") is a standard one-marker. Verified: for $q = 3.2\times10^{-7}$ C, $n = q/e = 2\times10^{12}$ and $\Delta m = n m_e = 1.8\times10^{-18}$ kg — recomputed below in Worked Example 1.

Go deeper · Derivation B · 1 minWhy charge looks continuous when it is actually grainy

Derivation BWhy charge looks continuous when it is actually grainy

Charge comes in steps of $e$ , yet every formula in the coming modules treats $q$ as a smoothly adjustable knob. We want to show when that is legitimate, by computing the relative size of one step of $e$ on a realistic laboratory charge. The strategy: take a typical static charge of $1\ \mu$ C, count its elementary charges, and compare one step against the total. The point to watch is the sheer size of the ratio — it is the same reason sand pours like a fluid.

Step 1. Count the grains in a microcoulomb: $N = \dfrac{10^{-6}}{1.6\times10^{-19}} = 6.25\times10^{12}$ elementary charges.

Step 2. The smallest possible change in this charge is one step of $e$ . Its relative size is $\dfrac{e}{q} = \dfrac{1.6\times10^{-19}}{10^{-6}} = 1.6\times10^{-13}$ — about one part in six trillion. Why this settles it: no instrument reading a microcoulomb resolves parts in $10^{13}$ ; the staircase is far finer than any measurement, so treating $q$ as continuous is exact for all practical purposes.

Step 3. Flip the logic to see where graininess does show: make the total charge small enough — a handful of $e$ — and the steps become the whole story. Millikan's oil drops carried $n = 1$ to $\sim 20$ elementary charges, so his measured drop charges landed on a visible ladder: $1.6, 3.2, 4.8\ (\times 10^{-19}\ \mathrm{C})$ — never in between. That ladder was the discovery of quantisation. Verified: $10^{-6}/1.6\times10^{-19} = 6.25\times10^{12}$ and $e/10^{-6}\ \mathrm{C} = 1.6\times10^{-13}$ , both recomputed.

Limiting cases

Case	Result	Meaning
$n = 1$	$q = e$ , one electron/proton	the graininess is the whole story — Millikan's regime
$q \gg e$ (lab scale)	steps of $e$ invisible ( $\sim$ 1 part in $10^{13}$ per $\mu$ C)	treating charge as continuous is exact in practice
$q_{\text{net}} = 0$	neutral — but full of balanced charge	neutral bodies still respond to charges nearby (next module)
system not isolated	charge crosses the boundary	conservation never fails — re-draw the boundary and the ledger balances
body loses electrons	$q > 0$ and mass decreases	"positive = lost electrons = lighter" — the double one-marker

Worked examples

Board level — counting transferred electrons (CBSE/NCERT pattern)

A polythene rod rubbed with wool acquires a charge of $-3.2\times10^{-7}\ \mathrm{C}$ . (a) How many electrons were transferred, and in which direction? (b) By how much does the mass of the rod change? ( $e = 1.6\times10^{-19}$ C, $m_e = 9.1\times10^{-31}$ kg.)

Step 1. Direction first, from the sign: the rod ended negative, so it gained electrons — they moved from the wool to the polythene. (State this in words; it carries a mark.)

Step 2. Count with quantisation, $q = ne$ : $n = \dfrac{|q|}{e} = \dfrac{3.2\times10^{-7}}{1.6\times10^{-19}} = 2.0\times10^{12}$ electrons. A whole number, as it must be.

Step 3. Mass change: the rod gained $n$ electrons, so its mass increased by $\Delta m = n\,m_e = (2.0\times10^{12})(9.1\times10^{-31}) = \boxed{1.8\times10^{-18}\ \mathrm{kg}}$ .

Step 4. The marks-scheme sentence: "Since the rod gains electrons, its charge is negative and its mass increases; the wool acquires an equal charge $+3.2\times10^{-7}$ C by conservation of charge." Both halves — equal-and-opposite partner charge, and the mass direction — are standard follow-up marks.

Competitive level — the impossible-charge filter plus contact sharing (NEET/JEE-Main pattern)

Two identical conducting spheres A and B carry charges $+6\ \mu\mathrm{C}$ and $-2\ \mu\mathrm{C}$ . They are brought into contact and separated. (a) Find the final charge on each. (b) How many electrons flowed, and which way? (c) Which of these could NOT be the charge on any isolated droplet: $3.2\times10^{-19}$ C, $2.4\times10^{-19}$ C, $8.0\times10^{-19}$ C?

Step 1. Contact between identical conductors shares the total equally (symmetry — neither sphere is special). Total $= +6 + (-2) = +4\ \mu$ C, so each sphere ends with $\boxed{+2\ \mu\mathrm{C}}$ . Conservation audited: $+2 + 2 = +4$ . ✓

Step 2. Electron flow: sphere B went from $-2\ \mu$ C to $+2\ \mu$ C, a change of $+4\ \mu$ C — meaning B lost electrons. Count: $n = \dfrac{4\times10^{-6}}{1.6\times10^{-19}} = \boxed{2.5\times10^{13}\ \text{electrons, from B to A}}$ .

Step 3. Quantisation filter: divide each option by $e$ . $3.2/1.6 = 2$ ✓; $8.0/1.6 = 5$ ✓; $2.4/1.6 = 1.5$ — not an integer, so $\boxed{2.4\times10^{-19}\ \mathrm{C}}$ is impossible. Timing note: 90 seconds. Part (a) is a 10-second symmetry read — "identical" is the licence to average, and without that word you cannot. The $n$ -count and the divisibility test are pure arithmetic; do the division as $q/e$ mantissas first ( $4/1.6 = 2.5$ ), then powers of ten.

Exam traps

Sign-of-transfer inversions. "Gains electrons" = negative = heavier; "loses electrons" = positive = lighter. Half the one-mark errors in this topic are one of these four words flipped. Write the electron arrow on your diagram before anything else.

Non-integer $n$ . Any answer for "number of electrons" that comes out fractional is wrong upstream — $n$ is a whole number by equation (3). Conversely, the "which charge is impossible?" MCQ is the divisibility test $q/e \in \mathbb{Z}$ ; NEET has recycled it for decades.

Unit conversions. $\mu$ C, nC and pC must become coulombs before any formula: $1\ \mu\mathrm{C} = 10^{-6}$ C, $1\ \mathrm{nC} = 10^{-9}$ C. The classic slip is carrying $\mu$ C into a force formula in the next module and landing $10^{12}$ off.

Averaging without the licence. Contact sharing splits the total equally only for identical conductors. Different sizes share unequally (the bigger sphere takes more — the full rule needs potential, coming in the Potential chapter). If the word "identical" is missing, the equal split is not available.

Adding magnitudes instead of algebra. Net charge of $+5\ \mu$ C and $-8\ \mu$ C is $-3\ \mu$ C, not $13\ \mu$ C. Additivity is a signed sum. (And net charge zero does not mean "nothing there" — see the warning above.)

Conservation misread as constancy. Conservation fixes the total of an isolated system, not the charge of each body. Bodies trade charge freely; the ledger's bottom line is what never moves. When charge "disappears" to damp air, the system boundary grew to include the air.

Constants per board. All Indian boards and NEET/JEE use $e = 1.6\times10^{-19}$ C and $m_e = 9.1\times10^{-31}$ kg unless the paper states otherwise; CIE and IB print constants on the data sheet — use their printed values, not your memorised ones.

Origins · 1 minBenjamin Franklin and how this was discovered

Benjamin Franklin

1706–1790 · Philadelphia

Printer, publisher, diplomat — and the person who turned electrical parlour tricks into bookkeeping. In the 1740s electricity meant rubbed rods and Leyden jars, described in a zoo of ad-hoc terms. Franklin proposed a ruthless simplification: a single electrical "fluid," with an excess called positive and a deficit called negative, whose total amount never changes. That last clause — stated plainly in his letters of 1747 — is the first clear statement of the conservation of electric charge, still exact today in every particle-physics experiment. His famous 1752 kite experiment (performed with more caution than legend suggests) identified lightning as the same electricity as the laboratory spark, uniting sky and bench under one ledger. His one guess that aged badly: which way the fluid flows. The mobile charge in metals turned out to be his "negative" — which is why conventional current and electron flow point opposite ways, an inconvenience every electronics student inherits from a coin-toss made three decades before the electron was found.

History

1733

— Charles du Fay shows electricity comes in two kinds ("vitreous" and "resinous"): like kinds repel, unlike attract.

1747

— Benjamin Franklin proposes the one-fluid picture, names the signs positive and negative, and states that total charge is conserved.

1785

— Charles-Augustin de Coulomb measures the force law between charges with his torsion balance — the next-but-one module of this chapter.

1897

— J. J. Thomson identifies the electron, the actual carrier of Franklin's "negative" fluid.

1913

— Robert Millikan's oil-drop experiment lands charges on a ladder of steps

1.6\times10^{-19}

C apart: quantisation measured directly.

2019

— The SI redefinition fixes

e

exactly at

1.602\,176\,634\times10^{-19}

C — the elementary charge becomes a defining constant of the unit system.

Going further

Texts. NCERT Physics Class 12, Ch. 1 §1.1–1.6 (the CBSE/NEET canonical statement of the four properties) · HC Verma, Concepts of Physics Vol 2, Ch. 29 · Halliday, Resnick & Walker Ch. 21 · CIE 9702 and IB Physics data booklets for the printed constants.

Provenance. Standard content per NCERT Ch. 1 and Halliday Ch. 21. A verifier should recompute: $n = 3.2\times10^{-7}/1.6\times10^{-19} = 2.0\times10^{12}$ ; $\Delta m = 2.0\times10^{12} \times 9.1\times10^{-31} = 1.8\times10^{-18}$ kg; $1\ \mathrm{C}/e = 6.25\times10^{18}$ ; $e/1\ \mu\mathrm{C} = 1.6\times10^{-13}$ ; sphere sharing $(+6-2)/2 = +2\ \mu$ C each with $4\ \mu\mathrm{C}/e = 2.5\times10^{13}$ electrons; $2.4/1.6 = 1.5$ (impossible), $3.2/1.6 = 2$ , $8.0/1.6 = 5$ .

Prerequisites. Atomic structure — protons and electrons (Class-10 science). Leads to. Charging Bodies: Conductors, Insulators & Induction (the methods this module's ledger makes possible) · Coulomb's Law (the force between the charges counted here).

Why can't a free particle have a charge of half an electron — what physically stops it?

Charge in ordinary matter is carried by whole electrons and protons, and you cannot transfer half an electron: the electron is (as far as every experiment shows) indivisible. Deeper down, protons are built of quarks with charges $\pm e/3$ and $\pm 2e/3$ , but the strong force confines quarks so that only integer-total combinations can exist in isolation. Searches for free fractional charges — in Millikan-style experiments run on tonnes of material — have all come up empty. So "what stops it" is two locks: electrons don't split, and quarks don't escape. For every exam: isolated charges satisfy $q = ne$ , full stop.

Is the choice of which charge is "positive" based on anything physical?

No — it is Franklin's convention from the 1740s, chosen decades before anyone knew electrons existed. He guessed that the mobile electrical fluid was what we now call positive; nature's mobile charge in metals turned out to be the electron, which therefore got the minus sign. Physics would be unchanged (and arguably tidier) with the labels swapped — conventional current and electron flow would then point the same way. What is not conventional: there are exactly two kinds, they cancel, and the proton and electron magnitudes match to at least one part in $10^{21}$ . The labels are ours; the structure is nature's.

If charge is conserved, why does my charged balloon go dead after an hour?

The balloon's charge didn't vanish — it moved. Air always contains some ions (made by cosmic rays and natural radioactivity), and humid air adds a thin conducting film of moisture to every surface; the balloon's excess electrons leak away ion by ion into the air and along whatever it touches. Draw the boundary around balloon plus surroundings and the total is unchanged to the last electron. This is also why electrostatics demos die on monsoon days and sparkle in dry winters: the leak rate, not the physics, changes with humidity.

Does a charged body really weigh a different amount? Could I measure it?

Really, but hopelessly beyond any balance. Charging transfers electrons of mass $9.1\times10^{-31}$ kg each; a hefty static charge of $1\ \mu$ C is $6.25\times10^{12}$ electrons, a mass shift of about $5.7\times10^{-18}$ kg — twenty orders of magnitude below what a good lab balance resolves. The exam interest is purely the sign: negative charging adds electrons (heavier), positive charging removes them (lighter). It's a logic test wearing a physics costume.

What carries charge in liquids and gases, where there's no fixed lattice?

Ions — atoms or molecules that have lost or gained electrons — and, in gases under strong fields, free electrons too. In salt water, Na⁺ and Cl⁻ drift in opposite directions; both directions of drift are real charge transport. This is why "only electrons move" is a rule about solids: in electrolytes, plasma, and your own nerve cells, positive carriers genuinely move. The bookkeeping rules of this module — additivity, conservation, quantisation — apply unchanged; only the identity of the courier changes.

How can a lightning bolt carry tens of coulombs when a balloon manages only nanocoulombs?

Scale and machinery. A thundercloud is kilometres across, with powerful updrafts acting as a conveyor that separates charge on colliding ice particles for minutes on end — a friction machine the size of a city running continuously. It accumulates tens of coulombs across the cloud before breakdown. Your balloon has square centimetres of contact and one rub. The comparison is the point: the coulomb is sized for currents (one ampere moves one coulomb per second through a wire), not for static rubbing, which is why electrostatics lives in nC and μC.

My textbook says charge is "invariant." Is that the same as "conserved"?

No — two different guarantees, both true. Conserved means the total doesn't change with time in an isolated system. Invariant means the value doesn't change with the observer: a charge measured as $e$ is $e$ whether it whizzes past you at 99% of light speed or sits still (contrast mass–energy, which observers disagree about). Invariance matters later, when moving charges become currents and magnetism; for this chapter, conservation is the workhorse. If an exam uses "invariant," it wants the observer statement, not the ledger statement.