Nature of Electric Charge

Electric charge is one of the most fundamental properties of matter. It is the reason your hair stands up after pulling off a wool sweater, why lightning bolts strike the earth, and why atoms hold together at all. Unlike mass, which is always positive, electric charge comes in two varieties — positive and negative — and it is this duality that makes electrostatics so rich and surprising. Every charged object you will ever encounter has a charge that is a whole-number multiple of a single, tiny unit called the elementary charge, e ≈ 1.602 × 10⁻¹⁹ C. This 'graininess' of charge is called quantisation. It means you can never find an isolated object carrying, say, 2.5e of charge — nature simply does not permit fractional multiples of e on free particles. Think of charge like money in a currency where the smallest coin is one cent: you can have any number of cents, but never half a cent. Charge is also strictly conserved and additive. The total charge of an isolated system never changes, and the net charge of a collection of objects is simply the algebraic sum of all individual charges. These two properties — quantisation and conservation — are cornerstones of modern physics, tested to extraordinary precision in particle accelerators and everyday circuits alike.

Key takeaways
  • Two Types of Charge
  • Quantisation of Charge
  • Conservation of Charge
  • Additivity of Charge
  • Invariance of Charge

Two Types of Charge

Benjamin Franklin's convention (still used today) labels the charge carried by a proton as positive (+) and the charge carried by an electron as negative (−). Like charges repel each other; unlike charges attract. A neutral atom has equal numbers of protons and electrons, so its net charge is exactly zero. When you rub a glass rod with silk, electrons transfer from the glass to the silk, leaving the glass positively charged and the silk negatively charged — charge is not created, only redistributed.

Quantisation of Charge

Charge is quantised: any observable charge Q must satisfy Q = n·e, where n is an integer (…−2, −1, 0, 1, 2, …) and e = 1.602 × 10⁻¹⁹ C is the elementary charge. Protons carry +e and electrons carry −e. Quarks inside protons and neutrons do carry fractional charges (±e/3 and ±2e/3), but quarks are permanently confined inside hadrons and never appear as free, isolated particles, so every observable free particle or macroscopic object has an integer multiple of e. Robert Millikan's famous oil-drop experiment (1909–1913) first measured e directly by balancing gravitational and electric forces on tiny oil droplets.

Conservation of Charge

In any isolated system, the total electric charge is constant. This is one of nature's exact conservation laws — no experiment has ever detected a violation. When an electron and a positron (anti-electron) annihilate, they produce two gamma-ray photons with zero charge, conserving the total charge of zero. When a nucleus undergoes beta-minus decay, a neutron (charge 0) becomes a proton (+e) plus an electron (−e) plus an antineutrino (0): the total charge before (0) equals the total charge after (+e − e + 0 = 0). Conservation applies even in nuclear and particle reactions.

Additivity of Charge

Charge is a scalar quantity (just a number with a sign). The net charge of any system is the algebraic sum of all individual charges: Q_net = q₁ + q₂ + q₃ + … For example, a system containing three protons and five electrons has Q_net = 3(+e) + 5(−e) = −2e ≈ −3.2 × 10⁻¹⁹ C. This additive property makes calculating the charge on macroscopic objects straightforward: even a tiny charged sphere typically carries billions of elementary charges, yet we simply sum them.

Invariance of Charge

Unlike mass, which increases with velocity according to special relativity, electric charge is Lorentz-invariant: the charge of a particle measured by any observer in any inertial frame is identical. A proton moving at 0.99c still carries exactly +e. This invariance is deeply connected to the symmetry of Maxwell's equations and to the fact that electromagnetic force laws remain consistent across reference frames.

The Key Equation

Q=ne,n∈Z,e=1.602×10−19 CQ = ne, \quad n \in \mathbb{Z}, \quad e = 1.602 \times 10^{-19}\,\text{C}
  • Q — Net electric charge (Coulomb (C)): The total charge of the object or system being considered.
  • n — Integer quantum number (dimensionless): Any whole number (positive, negative, or zero) counting the number of elementary charges.
  • e — Elementary charge (Coulomb (C)): The magnitude of charge carried by a single proton or electron; e ≈ 1.602 × 10⁻¹⁹ C.

Worked Example

Problem. A small plastic bead is found to carry a charge of −4.806 × 10⁻¹⁹ C. (a) How many elementary charges does this represent, and what type of charge excess does the bead have? (b) If this bead is touched to an identical neutral bead and then separated, what is the charge on each bead afterward?

n=−3,Q1=−2e≈−3.20×10−19 C,Q2=−e≈−1.60×10−19 Cn = -3,\quad Q_1 = -2e \approx -3.20\times10^{-19}\,\text{C},\quad Q_2 = -e \approx -1.60\times10^{-19}\,\text{C}

Answer. The original bead carries −3 elementary charges (3 excess electrons). After contact, the charges distribute as −2e and −e on the two beads respectively.

Figure
Diagram
Quantisation and Conservation of Electric ChargeNeutral3p⁺, 3e⁻Q = 02e⁻transferCharged3p⁺, 1e⁻Q = +2e0−2e−3e−e+e+2e+3eAllowed charge values (discrete multiples of e only)Conservation CheckBefore: 0 + 0 = 0After: (+2e) + (−2e) = 0 ✓
Origins · 1 minRobert Andrews Millikan and how this was discovered
RA
Robert Andrews Millikan
1868–1953 · American

Millikan performed the oil-drop experiment between 1909 and 1913, directly measuring the elementary charge e for the first time. By observing the equilibrium of gravitational and electric forces on charged oil droplets suspended between two plates, he deduced that charge always appeared in integer multiples of a single value — providing the first precise experimental evidence for the quantisation of charge. He was awarded the Nobel Prize in Physics in 1923. Millikan's original lab notebooks show he selectively reported data from drops that agreed with his expected value for e, discarding results he deemed 'unsteady' — an early famous example of confirmation bias in experimental physics, though his final answer was accurate.

  • Coulomb's Law — Coulomb's Law describes the electrostatic force between two charges, directly depending on the magnitude and sign of each charge covered here.
  • Electric Field — Electric fields are created by charges; understanding what charge is and how it is measured is the prerequisite for defining and calculating field strength.
  • Atomic Structure — Protons and electrons are the carriers of charge in matter; atomic structure explains how charge is distributed within atoms and how ions form.
  • Conductors and Insulators — The behaviour of charge in motion or at rest on materials depends fundamentally on how freely electrons can redistribute themselves, linking directly to charge properties.